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THE  DESIGN  OF  STATIC 
TRANSFORMERS 


[Frontispiece. 
View  of  assembling  department  in  a  transformer  manufacturing  works. 


THE 


DESIGN  OF  STATIC 
TRANSFORMERS 


BY 


H.  M.  HOBART,  M  INST.  C.E. 


NEW    YORK 

D.    VAN    NOSTRAND    COMPANY 

23    MURRAY   AND    27    WARREN    STREETS 

1911 


PREFACE 

THE  present  treatise  is  exclusively  of  a  practical  nature.  It 
constitutes,  however,  merely  a  brief  introduction  to  the  prac- 
tical aspects  of  transformer  design  and  construction.  If  the 
reader  has  not  already  acquired  a  knowledge  of  the  theory 
underlying  the  subject,  he  could  not  do  better  than  to  study 
either  Prof.  Gisbert  Kapp's  "  Transformers,"  or  Prof.  J.  A. 
Fleming's  "  The  Alternate-current  Transformer."  In  spite  of 
the  ten  years  which  have  intervened  since  the  publication  of 
the  last  edition  of  the  latter  work,  it  still  remains,  in  my 
opinion,  one  of  the  very  clearest  expositions  of  the  theory  of 
the  transformer.  My  own  work  in  this  field,  so  far  as  it  is  set 
forth  in  the  present  volume,  simply  deals  with  the  application 
to  practice  of  the  theory  so  admirably  set  forth  by  Profs. 
Fleming  and  Kapp  in  the  excellent  treatises  to  which  I  have 
referred.  Although  remarkably  few  books  have  been  written 
on  transformers,  nevertheless  there  exists  a  fairly  extensive 
literature  on  the  subject,  but  it  is  in  the  form  of  articles  and 
papers.  Amongst  the  most  noteworthy  recent  contributions 
may  be  mentioned  the  paper  by  Messrs.  A.  P.  M.  Fleming 
and  K.  M.  Faye-Hansen,  which  was  read  in  November,  1908, 
at  the  Institution  of  Electrical  Engineers,  and  the  paper  read 
in  June,  1909,  by  Mr.  E.  G.  Reed,  at  the  Thirty-second  Annual 
Convention  of  the  National  Electric  Light  Association. 

A  perusal  of  my  treatise  entitled  "  Electricity  "  (Constable 
&  Co.,  London,  1910),  will  assist  to  an  understanding  of  the 
terms  "power  factor."  ''inductance,"  "reactance"  and 
"  impedance,"  if  the  reader  is  not  already  clear  as  to  the 
meaning  of  these  terms. 

224493 


viii  PREFACE 

It  lias  been  deemed  desirable  that  the  present  work  should 
deal  with  the  fundamental  principles  of  practical  designing, 
but  so  soon  as  these  principles  have  been  assimilated,  the 
reader  should  proceed  to  study  carefully  the  many  essential 
constructional  details.  A  Bibliography  of  a  considerable 
number  of  papers  relating  to  static  transformers  is  given  at 
the  end  of  Chapter  I.  In  conclusion,  I  wish  to  acknowledge 
the  work  of  my  former  assistant,  Mr.  Evelyn  Good,  who 
carried  through  many  of  the  calculations,  under  my  direction, 
and  prepared  a  good  many  of  the  curves  and  diagrams.  My 
assistant,  Mr.  C.  Martin,  compiled  from  my  data  certain 
portions  of  Chapters  VIII.  and  IX.  My  thanks  are  due  to 
the  several  manufacturing  companies  whose  designs  are 
described  for  their  courtesy  in  providing  me  with  the  necessary 
information  and  for  photographs  and  drawings. 

H.  M.  HOBART,  M.  INST.  C.E. 

LONDON, 

December,  1910. 


TABLE  OF  CONTENTS 

CHAP.  PAGE 

FRONTISPIECE 

PREFACE .,                                   .  VJi 

LIST   OF   ILLUSTRATIONS  .  .  ....  .XI 

I.      INTRODUCTORY 1 

II.      THE   LEADING   DIMENSIONS   OF   A   TRANSFORMER   OF   A   GIVEN 

RATING .  .16 

III.  THE   CORE   LOSS   AND   THE   "ANNUAL   EFFICIENCY"           .        ...  59 

IV.  NO-LOAD   CURRENT,    POWER   FACTOR,    AND   EFFICIENCY    .            .  68 
V.      THE   DESIGN   OF   THE   WINDINGS   AND   INSULATION.            .  "        .  82 

VI.      THE   INFLUENCE   OF   FREQUENCY       .'.•'',.            .            .            .  88 

VII.      THE   REGULATION   OF   TRANSFORMERS        .           .           .           .           .  93 

VIII.      THE   HEATING   OF   TRANSFORMERS    .           ..           .           .           .    '       .  113 

IX.      TRANSFORMER   CASES   AND   TANKS    ..;;..  145 

X.      FORCED-COOLED   TRANSFORMERS  155 


LIST    OF    ILLUSTRATIONS 


FIG.  TITLE.  PAGE 

1.  Outline  Sketch  of  a  Eepresentative  Design   of  a   Core-type 

Single-phase  Transformer 17 

2.  Outline   Sketch  of  a   Representative  Design  of  a  Shell-type 

Single-phase  Transformer 18 

3.  Outline  Sketch  of  a  Type  of  Transformer  adapted  from  Dr. 

Kittler's  ' '  Handbuch  der  Elektrotechnik,"  1892          ,     .  ' .       19 

4.  Diagrammatic  Sketch  of  "  Berry  "  Transformer        .         .         .       21 

5.  1700-kva     25-cycle     Core-type      Three-phase    Westinghouse 

Transformer 22 

6.  100-kva    Single-phase    100  000-volt  Shell-type  Transformer, 

built  by  the  Westinghouse  Co.  for  the  Southern  Power  Co.       23 

7.  Curves  showing  Full-load  Efficiency  of  Single-phase  Trans- 

formers for  Different   Bated  Outputs,   Frequencies   and 
Primary  Voltages         .         .         .         .         .         .         .         k       25 

8.  Curves   showing  "  Yolts  per  Turn"  for  Single-phase  Trans- 

formers for  Different  Hated  Outputs,    Frequencies   and 
Primary  Voltages 27 

9.  Curves   showing   "  Volts  per  Turn  "  of  Single-phase  Trans- 

formers of  Different  Bated    Outputs    and    Periodicities. 
Curve  A— 50  Cycles  ;  Curve  B— 25  Cycles  ....       28 

10.  Saturation  Curve  of  Bepresentative  Sheet  Steel        ...       34 

11.  Hysteresis  Loss  Curves  for  Various  Periodicities  for  Old  High 

Loss  Sheet  Iron .35 

12.  Hysteresis  Loss  Curves  for  Various  Periodicities  for  Low  Loss 

Alloy  Steel 35 

13.  Eddy  Current  Loss  Curves  for  Various  Periodicities  for  Old 

Low  Besistance  Sheet  Iron 36 

14.  Eddy   Current   Loss    Curves    for    Various    Periodicities    for 

Modern  High  Besistance  Alloy  Steel 36 

15.  Total  Loss  Curves  for  Various  Periodicities  for  Old  High  Loss 

Sheet  Iron    ..........       37 

16.  Total  Loss  Curves  for  Various  Periodicities  for  Low  Loss  Alloy 

Steel 37 

17.  18.     Curves  showing  the  Belative  Hysteresis  and  Eddy  Current 

Loss  as  a  Percentage  of  the  Total  Loss  for  High  and  Low 

Loss  Steel 38 

19.  Curves  showing  the  Effect  of  Various  Kinds  of  Core  Insulation 
on  the  Nett  Effective  Iron  in  Transformer  Cores  for  Various 
Thicknesses  of  Stampings 44 


xii  LIST   OF   ILLUSTRATIONS 

FIG.  TITLE.  .       PAGE 

20,  21.     Types  of  Sections  of  Transformer  Cores       .  .         .45 

22 — 25.    Types  of  Sections  of  Transformer  Cores       ....       46 

26.  Core  Section  for  Elliptical-shaped  Coil 46 

27.  Curves  showing  the  Eelation  between  the  Output  and  the  Width 

of  Winding  Space 47 

28.  Section  of  20-kw  5000/200-volt  Transformer  Core  (Dimensions 

in  Centimeters) 48 

29.  Section  of  Winding  and  Core  of  20-kw  5000/200-volt  Trans- 

former (Dimensions  in  Centimeters)     .....       49 

30.  Simple  Concentric  Winding .51 

31.  Triple  Concentric  Winding 51 

32.  Sandwich  Winding •      .         .         .52 

33.  Simple  Concentric  Winding  with  Subdivided  Primary       .         .       52 

34.  35.     Curves  showing  Relation  between  Space  Factor  of  Winding 

Window  and  Bated  Output  for  Various  Primary  Voltages 
(Fig.  34,  Rectangular  Core  Section ;  Fig.  35,  Cruciform 
Core  Section)  .........  56 

36.  Sketch  of  Core  for  20-kw  5000/200-volt  50-cycle  Transformer  .       58 

37.  Annual   Efficiencies  of  20-kw  Transformers  at  Various  Load 

Factors 63 

38.  Profit  to  Electricity  Supply  Company  in  per  cent,  of  Cost  of 

Power  supplied  to  20-kw  Transformers  at  Various  Load 
Factors  .  .........  66 

39.  No-Load  Current  Diagram         .......       69 

40.  Curve  showing  Variation  of  Power  Factor  with  the  Load  for 

a  20-kw  Transformer  ........       72 

41.  42.     Characteristic  Curves  of  20-kw  Transformer  (Fig.  41,  Core 

Loss=190  watts;  Copper  Loss=36()  watts.  Fig.  42,  Core 
Loss= 360  watts;  Copper  Loss  =190  watts)  .  .  .73 

43.  Curves  showing  the  Relation  between  the  No-Load  Current 

and  the  Rated  Output  for  Transformers  having  (a)  High 
Grade  and  (b)  Ordinary  Grade  Laminations  ...  75 

44.  Curves  showing  the  Relation  between  the  Iron  Loss  and  the 

Rated  Output  for  several  Lines  of  Designs  for  different 
Periodicities  by  Various  Firms  A,  B,  C,  D  and  E  .  .  76 

45.  46.     Curves  showing  the  Influence  of  Varying  the  Periodicity 

and  Primary  Pressure  upon  the  Core  Loss  and  No-Load 
Current  of  a  20-kw  Transformer  .....  77 

47.  Curves   showing  the   Relation  between   the   Regulation  and 

the  Rated  Output  for  several  Lines  of  Designs  for 
Different  Periodicities  by  Firms  A,  B,  C  and  D  .  .  .79 

48.  Curves    showing  ratio    of    Labour    Cost    to   Cost    of    Active 

Material  for  Natural  Air-cooled  and  Oil-cooled  Trans- 
formers ..........  80 

49.  Outline  Drawing  showing  the  Arrangement  of  the  Windings 

of  the  20-kw  5000/200-volt  Transformer     .         .  .82 


LIST   OF  ILLUSTRATIONS  xiii 


50.  Sectional  Drawing  showing  Details  of  Primary  and  Secondary 

Windings  for  a  20-kw  5000/200-volt  Single-phase  Trans- 
former.        .         .         .         .         .         .         .         .         .         .83 

51.  Drawing  showing  Details  of  Primary  and  Secondary  Windings 

for  a  20-kw  5000/200-volt  Single-phase  Transformer  .         .       84 

52.  Curve  showing  Thickness  of  Insulation  between  Primary  and 

Secondary  Windings  of  Transformers  ....       86 

53—55.    Outline    Drawings  of    Transformers   for   20-kw    5000/200 

Volts  :  (a)  15  Cycles,  (b)  25  Cycles,  (c)  50  Cycles          .         .       92 

56.  Diagram   showing  Magnetic  Leakage    in    Core-type   Trans- 

former               ...       94 

57.  Diagram   showing   Magnetic   Leakage    in   Core-type    Trans- 

former         .         .         .         '         .         .         .         .         .         .95 

58.  Curve  of  Values  for  /  in  Formula  "  Percentage  Reactance  Drop 

a  t" 
=  fb~c  '     100 

59.  Transformer  Diagram  with  no  Reactance,  but  with  an  I  R  Drop 

of  15  per  cent.      .         .         .         .         .         .         .         .         .     101 

60.  Transformer  Diagram  with  30  per  cent.  Reactance  Drop  and 

15  per  cent.  I R  Drop.     Power  Factor=Unity    .         .         .102 

61.  Transformer  Diagram  with  30  per  cent.  Reactance  Drop  and 

15  per  cent.  772  Drop.  Angle  of  Lag  0=30°.  Cos  0=0,886     102 

62.  Transformer  Diagram  with  30  per  cent.  Reactance  Drop  and 

15  per  cent.  /  R  Drop.  Angle  of  Lag  0=63°.  Cos  0=0,440     103 

63.  Transformer  Diagram  with  30  per  cent.  Reactance  Drop  and 

15  per  cent,  7  R  Drop.  Angle  of  Lag  0=78°.   Cos  0=0,21  .     104 

64.  Transformer  Diagram  with  30  per  cent.  Reactance  Drop  and 

15  per  cent.  I R  Drop.    Angle  of  Lag  0=90°.    Cos  0=0      .     104 

65.  Variation  of  Drop  with  Power  Factor  and  Angle  of  Lag  .         .     105 

66.  Regulation  Diagram  of  '-0-kva  5000/200-volt  50-cycle  Single- 

phase  Transformer .         .106 

67.  Modified  Regulation  Diagram  of  20-kva  5000/200-volt  Single- 

phase  Transformer       .         .         .         .         .         .         .         .108 

68.  Regulation  Curves  of  20-kva  5000/200-volt  Single-phase  Trans- 

former  109 

69.  Arrangement  of  Coils  in  Core-type  Transformer  for  Three-wire 

Secondary    .         .         .         .         .         ...         .         .         .111 

70.  Arrangement  of  Coils  in  Core-type  Transformer  for  Three-wire 

Secondary Ill 

71.  Arrangement  of  Coils  in  Core-type  Transformer  for  Three-wire 

Secondary    .         .         .         .         .         .         .         .         .         .112 

72.  Air-cooled  Transformer      .         .         .         .         .         .         .         .114 

73.  Curve  showing  the  Time  taken  for  Transformers  of  Various 

Outputs  to  reach  Final  Temperature  at  Full  Load      .         .116 

74.  Heating  Curves  of  7, 5-kw  Transformer 117 

75.  40  000-volt  Oil-immersed  Transformer  118 


xiv  LIST   OF   ILLUSTEATIONS 

FIG.  TITLE.  PA(!E 

76.  Heating  Curves  of  Oil  Transformer.     (See  Fig.  77  for  Key  to 

Positions  of  Thermometers  for  Curves  A,  B,  C  and  D)         .     119 

77.  Diagram  showing  Positions  of  Thermometers  for  the  Heating 

Curves  shown  in  Fig.  76 120 

78.  Heating  Curves  for  5-kva  Transformer  in  Air  and  Oil.     Curve 

A  in  Case  without  Oil.     Curve  B  in  Case  with  Oil      .         .     121 

79.  Heating  Curve  for  50-kva  Transformer  in  Air  and  in  Oil  .     121 

80.  Curves  showing  Temperature  Eise  of  Transformers  in  Air  and 

in  Oil 122 

81.  Curve  showing  Time  for  50-kva  Transformer  to  reach  40°  C. 

at  Various  Loads 123 

82.  Curves  showing  Quantity  of  Oil  used  for  Single-phase  Trans- 

formers        .         .         .         .         .         .         .         .         .         .     137 

83.  Temperature  Curves  for  10-kva  Single-phase  Oil-cooled  Trans- 

former in  Small  and  Large  Cases 139 

84.  Cases  for    10-kva    Transformer    Temperature    Test,    showing 

Various  Positions  of  Thermometers      .         .         .         .         .140 

85.  Temperature  Test  on  a  10-kva  Single-phase  Transformer,  with 

a  Load  of  8  kw  (for  Positions  of  Thermometeis  Tl,  T2,  T3, 

see  Fig.  84) 142 

85A.  Elevation  of  Eibbed  Cast-iron  Case 146 

8oB.  Plan  of  Ribbed  Cast-iron  Case 147 

86.  Method  of  Jointing  the  Sides  and  Bottom  of  a  Transformer 

Case     .....  150 

87.  Westinghouse  1000-kva   100  000- volt  60- cycle   Oil-immersed 

Self-cooled  Transformer 152 

88.  Johnson   and  Phillips'  600-kva  Transformer  for  Oil  Immer- 

sion      153 

89.  Diagram    showing    Construction     of     an     Air-blast     Trans- 

former           .         .         .155 

90.  Coils  of  a  Shell-type  Air-blast  Transformer  after  Completion 

of  Impregnating  Process      .         .         .         .         .         .         .156 

91.  Diagrammatic   Sketch  of  American    General   Electric    Co.'s 

Air-blast  Transformers 157 

92.  550-kva  50-cycle  Air-blast  Transformer  by  the  Westinghouse 

Co 158 

93.  Diagram  showing  Arrangement  of  Transformers  and  Blowers  .     159 
91.     Bank  of  Air-blast  Transformers 160 

95.  10  000-kva  Oil-insulated  Water-cooled  Westinghouse  Trans- 

formers       .         .         .• 163 

96.  View  of  the  Interior -,of  the  American  General  Electric  Co.'s 

10  000-kva  100  000-volt  60-cycle  Design  for  a  Water- 
cooled  Oil  immersed  Transformer  before  the  Cooling  Coils 
have  been  Mounted 164 

97.  American    General    Electric     Co.'s    10  000-kva   100  000-volt 

Design  with  the  Cooling  Coils  in  Place       .         .         .         .     165 


LIST   OF   ILLUSTRATIONS  xv 


98.  Westinghouse   Oil-insulated  Water-cooled   Transformer   for 

High  Pressure  and  Small  Current 166 

99.  Westinghouse   Oil-insulated   Water-cooled   Transformer  for 

Low  Pressure  and  Large  Current 167 

99 A.  1800-kva  Water-cooled  Oil-immersed  Transformer,  built  by 

the  American  General  Electric  Co.       .         .         .         .         .168 

100.  Oil-immersed  Transformer  provided  with  Cylindrical  Barrier 

to  promote  Circulation         .         .         .         .         .         .         .172 

101.  Forced  Oil-cooled  Transformer  and  Accessory  Plant       .         .173 


THE    DESIGN    OF    STATIC 
TRANSFORMERS 


CHAPTEE  I 

INTRODUCTORY 

A  PAPER  by  Mr.  George  Westinghouse,  entitled  "  The 
Electrification  of  Kailways,"  was  read  at  a  recent1  meeting  of 
the  Institution  of  Mechanical  Engineers.  The  paper  was 
prefaced  by  the  following  paragraph  : — 

"As  an  illustration  of  the  wonders  of  the  laws  of  nature, 
few  inventions  or  discoveries  with  which  we  are  familiar  can 
excel  the  static  transformation  of  the  electrical  energy  of 
alternating  currents  of  high  pressure  into  their  equivalent 
energy  at  a  lower  pressure.  To  have  discovered  how  to  make 
an  inert  mass  of  metal  capable  of  transforming  alternating 
currents  of  100  000  volts  into  currents  of  any  required  lower 
pressure  with  a  loss  of  only  a  trifle  of  the  energy  so  trans- 
formed, would  have  been  to  achieve  enduring  fame.  The  facts 
divide  this  honour  among  a  few,  the  beneficiaries  will  be  tens 
of  millions." 

At  a  later  point  in  his  paper,  Mr.  Westinghouse  writes  as 
follows  : — 

"  I  was  led  in  1885,  to  interest  myself  in  the  American 
patents  of  Gaulard  and  Gibbs  (a  Frenchman  and  an  English- 
man), covering  a  system  of  electrical  distribution  by  means  of 

1  July  29, 1910. 
S.T.  B 


2     l  THE   DESIGN '  OF  '  STATIC   TKANSFORMERS 

alternating  currents,  with  static  transformers  to  reduce  these 
currents  from  the  high  pressure  necessary  for  the  economical 
transmission  of  electrical  energy  to  the  lower  pressures  required 
for  the  operation  of  incandescent  lamps  and  for  other  purposes. 
No  inventions  ever  met  with  greater  opposition  in  their  com- 
mercial development  than  those  relating  to  the  generation, 
distribution  and  utilisation  of  alternating  currents." 

The  zeal  displayed  twenty-five  years  ago  by  Mr.  Westing- 
house  in  the  matter  of  the  introduction  and  the  extension  of 
systems  employing  alternating  electricity  has  continued  down 
to  the  present  day,  and  while,  in  my  opinion,  one  result  has 
been  to  employ  alternating  electricity  in  a  good  many  instances 
where  continuous  electricity  would  have  afforded  the  more 
economic  solution,  nevertheless  the  engineering  profession  is 
in  no  small  measure  in  Mr.  Westinghouse's  debt  for  the 
immense  progress  made  in  the  last  twenty-five  years  in  the 
use  of  alternating  electricity  and  in  the  development  of  the 
static  transformer. 

It  must  not  be  concluded  that  America  was  the  principal 
scene  of  the  early  development  of  the  static  transformer.  On 
the  contrary,  in  Dr.  J.  A.  Fleming's  "  Alternate  Current 
Transformer,"  the  first  edition  of  which  was  published  in 
1889,  will  be  found  a  record  of  work  done  in  England  on  a 
larger  scale  than  had  at  that  time  been  approached  in 
America.  The  volumes  of  the  Journal  of  the  Institution  of 
Electrical  Engineers,  for  the  years  from  1888  to  1892  (Vois. 
XVII.  to  XXI.),  contain  a  number  of  papers  which  are  of 
very  great  interest  as  bearing  upon  developments  during  the 
period  when  alternating  electricity  was  first  being  introduced 
on  a  large  commercial  scale.  Amongst  these  papers  may  be 
mentioned:  "  Alternate  -  current  Transformers,"  by  Kapp  ; 
"  Central  Station  Lighting  :  Transformers  v.  Accumulators," 
by  Crompton ;  "  Alternate-current  Working,"  by  Mordey ; 
"  Transformer  Distribution,"  by  James  Swinburne ;  "  On 
some  Effects  of  Alternating-current  Flow  in  Circuits  having 


INTRODUCTORY  3 

Capacity  and  Self-induction,"  by  J.  A.  Fleming;  "Some 
Experimental  Investigations  of  Alternating  Currents,"  by 
Alexander  Siemens ;  "  Experimental  Researches  on  Alternate- 
current  Transformers,"  by  J.  A.  Fleming. 

There  could  be  no  better  introduction  to  the  subject  than 
that  afforded  by  a  careful  study  of  these  seven  papers  and  more 
especially  of  the  discussions  to  which  they  gave  rise.  Some 
twenty  years  have  since  elapsed,  and  the  present  treatise  is 
largely  based  on  the  work  of  those  who,  profiting  by  the 
pioneer  investigations  of  Crompton,  Ferranti,  Fleming,  Forbes, 
Kapp,  Mordey,  Siemens,  Swinburne,  Silvanus  Thompson  and 
Elihu  Thomson,  have  carried  on  the  more  prosaic  task  of 
developing  the  commercial  transformer  of  the  present  day. 

My  first  intimate  acquaintance  with  the  static  transformer 
was  formed  in  1889  when,  under  the  torrid  blaze  of  a  bank  of 
incandescent  lamps  which  constituted  the  "  load,"  I  spent  a 
month  or  so  at  the  daily  task  of  pulling  little  truck-loads  of 
transformers  into  place  against  the  wall  of  the  testing  room, 
measuring  their  "  cold "  resistance,  connecting  up  their 
primaries,  "  flashing  "  their  secondaries  for  polarity — ousting 
from  the  sacred  premises  those  found  in  various  respects 
unsound,  and  subjecting  the  survivors  to  a  "  load  "  test  for 
some  specified  number  of  hours.  This  process  \vas  followed  by 
a  measurement  of  the  "  hot  "  resistance  and  by  the  registering 
of  each  transformer's  number  and  test  results  in  a  record  book. 
The  largest  of  these  transformers  was  only  some  7  or  8  kw,  and 
the  most  usual  sizes  were  those  of  but  a  couple  of  kilowatts  rated 
capacity.  They  were  nearly  all  for  a  periodicity  of  125  cycles 
per  second,  and  the  primaries  were  usually  wound  so  that  they 
could  be  connected  either  for  1000  or  2000  volts,  the  secondaries 
usually  being  connected  to  give  either  52  or  104  volts  on  no  load. 
The  measuring  of  the  core  loss  was  no  part  of  my  task  ;  indeed 
1  strongly  suspect  that  but  little  attention  was  then  given  to 
any  such  obscure  detail.  A  year  or  so  later  found  me  renewing 
my  acquaintance  with  static  transformers.  This  time  the 


4       THE   DESIGN   OF    STATIC   TEANSFOEMEES 

scene  was  an  instrument  calibrating  and  experimental  depart- 
ment. Our  duties,  so  far  as  related  to  transformers,  comprised 
testing  the  insulation  resistances  between  primaries  and 
secondaries  and  "to  frame,"  of  transformers  of  various  sizes 
and  types.  We  duly  reported  on  the  insulation  resistance, 
which,  in  those  early  days,  was  often  so  low  as  to  be  well  within 
the  range  of  a  very  unsensitive  testing  set.  On  transformers 
of  other  than  our  own  firm's  manufacture  we  made  core-loss 
measurements,  estimated  the  weights  of  copper  andiron  and 
sometimes  ascertained  the  numbers  of  turns  and  other  particu- 
lars of  the  windings. 

The  subject  of  core  loss  gradually  came  prominently  to  the 
front  and  for  a  long  time  we  were  fully  occupied  in  studying  the 
methods  and  results  set  down  in  Ewing's  "  Magnetic  Induction 
in  Iron  and  Other  Metals,"  and  in  ourselves  making  ballistic 
tests  of  sheet  iron  and  steel.  The  facilities  of  our  department 
were  placed  at  the  disposal  of  the  company's  purchasing  agent, 
who  was  scouring  the  world's  markets  for  suitable  sheet  iron.  I 
well  remembered  that  it  was  not  long  before  we  ascertained  that 
the  cheapest  grades  of  material  often  had  (if  annealed  from  a 
suitably  high  temperature)  the  lowest  core  loss  and  that 
plates  rolled  from  Swedish  soft  charcoal-iron,  while  they  cost 
much  more,  were  no  better  as  regards  core  loss  than  were  the 
cheap  grades  of  sheet  steel  used  for  various  non-electrical  com- 
mercial purposes,  such,  if  I  remember  rightly,  as  shipper's  labels. 
The  chief  difficulty  consisted  in  obtaining  in  great  quantity 
material  of  the  good  quality  of  the  occasional  sample.  But 
even  our  best  results  of  that  time  (1890  and  1891)  related  to 
materials  which  were  far  inferior,  as  regards  core  loss,  to  the 
low-loss  alloys  at  present  (1910)  employed,  and  were  also  much 
more  prone  to  "  ageing."  Contemporaneously  with  the  testing 
of  magnetic  materials,  we  were  required  to  make  tests  of  the 
core  losses  of  completed  transformers,  for  by  this  time  (1891) 
our  company's  designers  were  becoming  keenly  alive  to  the 
importance  of  keeping  down  the  core  losses  and  were  engaged 


INTKODUCTOEY  5 

in  modifying  their  designs  as  regards  the  proportions  of  the 
magnetic  and  copper  circuits.  At  that  time  we  measured 
these  core  losses  by  dynamometer-wattmeters  of  the  Siemens 
pattern.  Inconsistencies  in  the  measurements  compelled  us  to 
turn  our  attention  to  the  study  of  errors  in  wattmeters,  and 
we  were  led  to  realise  the  importance  of  "  swamping "  the 
inductance  of  the  pressure  coil  by  the  use  of  very  high  resist- 
ances, wound  non-inductively,  in  series  with  the  pressure  coil. 
This,  of  course,  involved  weaker  forces  and  the  use  of  weaker 
torsion  springs.  The  friction  of  the  contacts  dipping  in  the 
mercury  cups  constituted  an  annoying  source  of  error.  We 
were  guided  through  these  difficulties  to  no  inconsiderable 
extent  by  the  inspiring  co-operation  of  Mr.  Ernst  Danielson, 
who  had  then  (1891  and  1892)  joined  the  company  by  whom 
I  was  employed.  Danielson  encouraged  me  to  study  Dr. 
Fleming's  "  Alternate-current  Transformer  "  and  to  draw  vector 
diagrams,  in  the  way  explained  by  Fleming,  for  the  actual  cases 
of  certain  of  our  firm's  transformers. 

Among  various  interesting  transformers  of  other  firms  which 
came  through  our  hands,  I  well  remember  a  Swinburne  hedge- 
hog transformer.  A  certain  transformer  from  another  firm, 
interested  me  deeply  at  the  time.  This  transformer  had  fully 
twice  as  much  iron  and  twice  as  much  copper  as  the  more  usual 
designs,  and  although  the  material  of  the  core  was  of  excellent 
magnetic  qualit}7,  this  lavish  expenditure  for  active  material 
had  been  so  ill-utilised  that  both  the  core  loss  and  the 
regulation  of  this  transformer  were  much  worse  than  for  a 
transformer  of  the  more  usual  proportions.  Such  instances 
contain  very  important  lessons  for  engineers. 

The  next  "  discovery  "  which  then  impressed  me,  and  still 
impresses  me,  as  being  of  especially  striking  importance  was 
brought  about  as  follows  :  It  had  then  come  to  be  the  custom 
for  the  transformer-designing  department  to  make  its  own 
core-loss  tests,  merely  bringing  the  dynamometers  to  the 
instrument  room  in  order  that  we  should  calibrate  them  at 


6       THE   DESIGN   OF    STATIC   TEANSFOEMEES 

intervals  and  record  their  "  constants."  One  day  we  were 
accused  of  having  given  out  the  constant  of  one  of  these 
wattmeters  as  10  per  cent,  too  low  ;  for  a  certain  standard 
transformer,  which  was  kept  permanently  in  the  testing  room, 
was  remeasured,  and  the  readings  indicated  a  core  loss  some 
10  per  cent,  less  than  its  known  value  as  determined  by  many 
previous  measurements.  We  investigated  the  instrument 
carefully,  but  could  only  confirm  our  original  calibration. 
During  two  or  three  days  we  did  little  else  than  overhaul 
standards  and  check  instruments  against  one  another.  Then 
it  was  definitely  found  that  the  same  wattmeter  at  certain 
times  indicated  the  core  loss  of  a  given  transformer  to  be 
10  per  cent,  greater  than  at  other  times.  Further  investiga- 
tions disclosed  the  fact  that  the  low  readings  were  obtained 
when  the  circuits  were  supplied  from  an  alternator  with  its 
armature  windings  embedded  in  slots,  while  the  high  readings 
were  obtained  when  an  alternator  was  used  whose  armature 
windings  consisted  of  flat  coils  resembling  "  pancakes "  and 
bound  down  on  the  surface  of  the  armature.  Thus  the  watt- 
meter was  vindicated,  and  we  were  impressed  with  the 
practical  significance  of  the  shape  of  emf  wave  supplied  by 
an  alternator.  The  slotted  alternator  was  one  of  the  earliest 
which  our  firm  had  built.  It  was,  of  course,  a  single*-phase 
machine,  and  it  had  only  one  slot  per  pole.  This  gave  it  a 
very  "peaked"  wave.  We  confirmed  this  by  determining  by 
the  Joubert  contact  method  (using  our  Thomson  quadrant 
electrometer)  the  wave  shapes  of  both  machines  not  only  on 
no  load,  but  also  on  full  load.  The  old  "pancake"  or 
"  smooth-core  "  type  had  practically  a  sine  wave  both  at  no 
load  and  at  full  load,  while  the  wave  of  the  iron -clad  alter- 
nator was  very  peaked  under  both  conditions,  and  (for  a  given 
terminal  pressure)  had  a  crest  pressure  some  10  per  cent, 
higher  than  the  crest  pressure  of  the  "  smooth-core  "  alter- 
nator. In  other  words,  the  form  factor  (defined  by  Fleming 
on  p,  583  of  Vol,  L  of  the  2nd  edition  of  his  "  Alternate-current 


INTEODUCTOEY  7 

Transformer  "  as  the  ratio  of  the  root-mean-square,  or  virtual 
value,  to  the  true  mean  or  average  value)  was  10  per  cent, 
higher  for  the  iron-clad  machine  than  for  the  smooth-core 
machine.  Some  firms  at  that  time  took  advantage  of  the 
lower  core  loss  obtained  on  such  uni-slot  machines.  The  core 
losses  which  they  quoted  for  their  transformers  were  such  as 
would  be  obtained  when  the  "  form  factor "  was  at  least 
10  per  cent,  higher  than  that  of  a  sine-wave  alternator.  The 
form  factor  of  a  sine  wave  is  1,11,  and  the  form  factors  of 
these  uni-slot  single-phase  alternators  were  usually  at  least 
(1,10  X  1,11  =)  1,22.  It  is  highly  important  that  the  present- 
day  student  should  have  these  points  well  in  mind,  since  they 
are  apt  to  be  less  appreciated  when  read  from  books  than 
when,  as  in  our  case,  they  were  obtained  at  first  hand  by 
experiences  which  at  the  time  were  actually  distressing. 
While  the  modern  alternator  is  usually  required  to  supply  a 
sine  wave  of  pressure,  nevertheless  various  conditions  tempo- 
rarily occurring  in  electrical  networks  often  occasion  a  very 
considerable  distortion  of  the  wave  form.  It  is  certainly 
decidedly  important  to  specify  that  core  losses  shall  be 
measured  from  a  circuit  supplying  a  sine  wave  of  pressure. 
The  unravelling  of  this  10  per  cent,  discrepancy  in  the  way 
in  which  it  was  encountered  at  our  works  was  largely  due  to 
Danielson's  insight. 

Up  to  this  time  (1892)  our  transformers  had  almost  all  been 
designed  for  125  cycles  and  for  a  lighting  load,  i.e.,  for 
supplying  incandescent  lamps.  Owing  to  the  non-inductive 
character  of  this  load,  there  had  been  no  occasion  to  devote 
any  special  attention  to  decreasing  the  inductance  of  the 
windings.  The  problem  of  transformer  design  had  related 
chiefly  to  combining  a  minimum  mean  length  of  magnetic 
circuit  with  a  minimum  mean  length  of  turn  of  the  winding. 
In  the  commercial  development  of  the  polyphase  induction 
motor,  which  became  an  important  matter  in  1892  and  1893, 
it  was  soon  found  quite  impossible  to  employ  these  lighting 


8       THE   DESIGN   OF    STATIC   TKANSFOKMEKS 

transformers  with  good  effect.  It  was  not  at  first  clearly 
appreciated  that  the  non-intermixing  of  the  primary  and 
secondary  coils  was  so  especially  a  fault ;  on  the  contrary,  it 
was  considered  that  the  difficulties  were  due  to  the  increased 
saturation  of  the  core  accompanying  the  use  of  these  125-cycle 
transformers  on  the  60-cycle  circuits,  which  were  at  first 
usually  employed  for  power  purposes.  For  the  same  terminal 
pressure  halving  the  periodicity  doubled  the  flux  required  in 
the  magnetic  circuit.  This  did  not  so  greatly  increase  the 
core  loss,  since  the  doubled  density  was  partly  offset  by  the 
halved  periodicity  ;  in  fact,  the  core  loss  was  only  increased 
by  some  35  per  cent,  by  employing  the  same  transformer  at 
the  same  pressure,  but  on  a  circuit  of  half  the  periodicity. 
But  these  transformers  had  not  been  sufficiently  liberally 
designed  to  permit  of  this  35  per  cent,  increase  in  the  core 
loss,  and  there  was  also  in  some  cases  the  further  trouble  of 
greatly  increased  magnetising  current  due  to  the  greater 
saturation.  The  enunciation  at  about  this  time  of  the  one- 
and-sixth-tenths  power  law  of  hysteresis  by  Dr.  C.  P.  Steinmetz 
was  very  opportune,  and  was  of  great  assistance  in  transformer 
design.  In  placing  on  the  market  transformers  of  lower 
periodicity  for  power  work,  in  order  to  avoid  the  necessity 
for  new  parts  throughout,  the  same  general  type  (the  shell 
type)  was  retained  and  the  same  general  proportions  of  the 
winding  space,  but  occasion  was  taken  to  intermix  to  a 
moderate  extent  the  primary  and  secondary  coils,  so  as  to 
decrease  the  inductive  drop,  i.e.,  so  as  to  obtain  closer  pressure 
regulation  with  inductive  loads. 

The  incursion  into  the  power  field  rapidly  led  to  requiring 
transformers  of  larger  size  and  introduced  great  difficulties 
in  the  matter  of  so  designing  the  transformers  that  they 
should  not  overheat.  The  years  1893  and  1894  saw  the 
extensive  commercial  introduction  of  the  principle  of  immersing 
the  transformer  in  oil.  No  inconsiderable  difficulties  were 
experienced  in  obtaining  a  suitable  oil,  and  a  great  deal  of 


INTRODUCTORY  9 

experimenting  was  done  before  a  commercial  stage  was  reached. 
The  matter  was  chiefly  worked  out  by  Mr.  W.  S.  Moody,  to 
whom  (and  also  to  Prof.  Elihu  Thomson)  the  development  of 
not  only  the  oil  transformer,  but  also  the  air-blast  transformer 
(which  was  developed  simultaneously)  was  in  great  measure 
due.  At  this  time  (1893  to  1895)  there  was  a  rapid  increase 
in  the  pressures  employed  in  transformers.  Up  to  1892 
pressures  of  2000  to  3000  volts  had  only  been  exceeded  in 
special  cases,  but  during  the  immediately  following  years, 
pressures  of  10  000  and  even  20  000  volts  were  fairly  fre- 
quently employed,  and  the  general  experience  then  was  that 
these  pressures  could  be  best  handled  with  the  air-blast  type 
of  design.  As  the  reader  knows,  transmission  plants  are  now 
(1910)  in  operation  where  the  transformers  are  wound  for 
pressures  of  80  000  and  even  100  000  volts,  but  in  1894  a 
pressure  of  20  000  volts  was  considered  distinctly  high.  In 
America  the  manufacturers  did  not  then  build  three-phase 
transformers,  but  employed  groups  of  three  single-phase 
transformers. 

Another  variant  introduced  by  this  time  (1894  to  1895)  was 
the  increasing  use  of  the  low  periodicity  of  25  cycles  per 
second.  This  was  chiefly  brought  about  by  the  bad  expe- 
riences obtained  with  50-cycle  and  60-cycle  rotary  converters. 
For  installations  where  rotary  converters  were  likely  to  be 
required  it  became  usual  to  employ  25  cycles  per  second,  and 
this  periodicity  has  ultimately  found  very  considerable  favour, 
as  it  permits  of  advantages  in  transmission-line  design  and 
also  in  other  directions,  especially  as  regards  the  constants  of 
the  designs  of  generators  and  motors. 

It  was  not  until  1895  that  I  was  first  given  a  really  con- 
siderable amount  of  responsible  transformer  designing.  But 
these  earlier  episodes  had  afforded  a  good  preliminary  train- 
ing, and  I  took  on  the  task  with  much  interest.  But  it  is 
only  when  one  comes  right  down  to  doing  the  actual  task 
that  one  is  capable  of  fully  appreciating  the  magnitude  of  it, 


10     THE   DESIGN   OF    STATIC   TRANSFORMERS 

and  although  I  have  designed  large  numbers  of  transformers 
during  the  last  fifteen  years,  nevertheless  the  prospect  as 
regards  as-yet-unworked  possibilities  broadens  with  each 
successive  year,  and  I  am  each  year  more  certain  that  the 
subject  of  transformer  design  cannot  be  covered  by  the 
enunciation  of  rules,  formulas  and  constants,  but  that  the 
designing  of  a  transformer  or  of  a  line  of  transformers  for  any 
particular  rating  or  ratings  still  affords,  and  will  for  many 
years  continue  to  afford,  ample  scope  for  careful  thought  and 
work.  It  is  not  in  contradiction  to  this  view  that  I  put  forward 
in  the  course  of  this  treatise  various  rules  and  tables,  but 
rather  that  they  may  be  employed  as  rough  starting  points, 
and  in  the  full  realisation  that  it  is  often  not  only  expedient, 
but  in  the  interests  of  obtaining  the  best  results  that  wide 
departures  from  these  preliminary  indications  should  be  made 
as  the  design  proceeds. 

I  should  like  to  direct  special  attention  to  the  almost  pre- 
dominating importance  in  transformer  design  and  construction 
of  the  selection  and  testing  of  materials.  We  have  to  consider 
not  only  that  the  materials  shall  be  initially  of  the  correct 
quality,  but  that  they  shall  not  "  age."  It  was  Mr.  G.  W. 
Partridge  who,  some  twenty  years  ago,  first  directed  attention 
to  the  "  ageing  of  transformers."  No  less  important  is  the 
question  of  deterioration  of  the  insulating  materials,  and  of  the 
cooling  oil  in  which  the  transformer  is  immersed.  There  are 
also  exceedingly  difficult  questions  of  the  effects  of  the  oil  on 
the  insulating  materials,  and  these  effects  render  certain  other- 
wise-excellent insulating  materials  quite  unsuitable  for  oil 
transformers. 

The  Epstein  method  of  testing  iron  has  been  adopted  in 
Germany  and  constitutes  the  basis  for  contracts  for  the  supply 
of  core  plates.  In  this  country  contracts  are  much  less  definite 
on  this  point,  and  it  would  be  of  great  advantage  to  adopt 
the  Epstein  method. 

The  present  treatise  should  be  regarded  as  merely  an  intro- 


INTRODUCTORY  11 

duction  to  the  practical  designing  of  transformers,  and  the  reader 
should  realise  that  there  are  many  matters  of  great  importance 
which  have  not  been  included.  The  briefest  description  of  these 
numerous  very  important  subjects,  such  as  the  mechanical 
stresses  in  the  windings,  the  insulation  of  extra-high-pressure 
transformers,  the  design  of  terminals  and  bushings,  corona 
phenomena,  the  testing  of  sheet  steel  for  transformer  cores,  the 
testing  of  transformer  oil,  the  extra  insulation  of  the  end  turns 
(which  are  subjected  to  excess  pressures  at  the  instant  of 
switching  in),  ground  shields  and  other  protective  devices,  the 
question  of  employing  three  single-phase  or  one  three-phase 
transformer,  the  use  of  the  "delta"  or  "  Y  "-connection  of 
three-phase  transformers,  and  the  subject  of  single-coil 
transformers  (sometimes  known  as  compensators  or  auto-trans- 
formers), as  distinguished  from  transformers  with  distinct 
primary  and  secondary  windings,  would  have  necessitated  a 
treatise  far  larger  and  more  expensive  than  this  little  intro- 
ductory volume.  I  have  confined  my  discussion  of  the  subject 
to  those  points  regarding  which  a  reasonable  approach  to 
definite  designing  methods  is  practicable,  and  I  believe  that  I 
have  supplied  a  link  which  has  not  existed,  at  any  rate  in  a 
form  which  has  met  the  needs  of  students,  who,  although  they 
understand  the  underlying  theory,  are  at  a  loss  how  to  proceed 
when  called  upon  to  work  out  an  actual  design.  With  a  view 
to  facilitating  the  further  study  of  the  static  transformer,  I  am 
concluding  this  introductory  chapter  with  a  brief  bibliography 
of  some  useful  papers  on  the  subject,  and  I  am  of  opinion  that 
after  completing  his  study  of  the  pres.ent  treatise,  the  reader 
will  be  in  a  position  to  consult  with  advantage  the  papers 
therein  mentioned. 


12     THE   DESIGN   OF    STATIC   TBANSFOKMERS 

A  BIBLIOGEAPHY  OF  A  NUMBEE  OF  IMPOETANT  PAPEES 
WHICH  HAYE  BEEN  PUBLISHED  DUEING  THE  LAST 
TWENTY-THEEE  YEAES  ON  THE  SUBJECT  OP  THE 
STATIC  TEANSFOEMEE. 

1888. 

GISBERT  KAPP. — On  Alternate -current  Transformers.  (Journ.  Inst. 
Elec.  Engrs.,  Vol.  17,  p.  96.) 

E.  E.  B.  CROMPTON.— Central  Station  Lighting ;  Transformers  v. 
Accumulators.  (Journ.  Inst.  Elec.  Engrs.,  Yol.  17,  p.  349). 

1889. 

W.  M.  MOEDEY. — Alternate -current  Working.  (Journ.  Inst.  Elec. 
Engrsi,  Yol.  18,  p.  583.) 

H.  J.  EYAN. — Transformer  Curves.  (Trans.  Am.  Inst.  Elec.  En^-rs., 
Yol.  6.) 

1891. 

JAMES  SWINBURNE. — Transformer  Distribution.  (Journ.  Inst.  Elec. 
Engrs.,  Yol.  20,  p.  163.) 

DR.  J.  A.  FLEMING.— On  Some  Effects  of  Alternating-current  Flow  in 
Circuits  having  Capacity  and  Self-induction.  (Journ.  Inst.  Elec.  Engrs., 
Yol.  20,  p.  362.) 

NIKOLA  TESLA. — Experiments  with  Alternate  Currents  of  Yery  High 
Frequency.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Yol.  8,  p.  267.) 

1892. 

ALEXANDER  SIEMENS. — Some  Experimental  Investigations  of  Alternate 
Currents.  (Journ.  Inst.  Elec.  Engrs.,  Yol.  21,  p.  164.) 

DR.  J.  A.  FLEMING. — Experimental  Eesearches  on  Alternate-current 
Transformers.  (Journ.  Inst.  Elec.  Engrs.,  Yol.  21,  p.  594.) 

C.  P.  STEINMETZ.— On  the  Law  of  Hysteresis.  (Trans.  Am.  Inst. 
Elec.  Engrs.,  Yol.  9,  pp.  3  and  621.) 

1893. 

C.  P.  STEINMETZ.— Note  on  the  Disruptive  Strength  of  Dielectrics. 
(Trans.  Am.  Inst.  Elec.  Engrs.,  Yol.  10,  p.  64.) 

FREDERICK  BEDELL. — Hedgehog  Transformer  and  Condensers.  (Trans. 
Am.  Inst.  Elec.  Engrs.,  Yol.  10,  p.  513.) 

1895. 

C.  P.  STEINMETZ. — Theory  of  the  General  Alternating  Transformer. 
(Trans.  Am.  Inst.  Elec.  Engrs.,  Yol.  12,  p.  245.) 

1896. 

BEETON,  TAYLOR  AND  BARR.— Experimental  Tests  on  the  Influence  of 
the  Shape  of  the  Applied  Potential  Difference  Wave  on  the  Iron  Losses 
of  Transformers.  (Journ.  Inst.  Elec.  Engrs.,  Yol.  25,  p.  474.) 


INTKODUCTOKY  13 

C.  K.  HUGUET.— An  Analysis  of  Transformer  Curves.  (Trans.  Am. 
Inst.  Elec.  Engrs.,  Vol.  13,  p.  207.) 

1898. 

W.  F.  WHITE. — Alternating  -current  Transformers  from  the  Station 
Manager's  View-point.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  15,  p.  505.) 

F.  W.  CARTER.— The  Design  of  Transformers.  (Trans.  Am.  Inst.  Elec. 
Engrs.,  Vol.  15,  p.  639.) 

1899. 

W.  L.  EOBB. — Series  Arc  Lighting  from  Constant-current  Trans- 
formers. (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  16,  p.  533.) 

1903. 

F.  0.  BLACKWELL. — Y  or  A  Connection  of  Transformers  (Trans.  Am. 
Inst.  Elec.  Engrs.,  Vol.  22,  p.  385.) 

1904. 

E.  W.  EICE,  JR. — The  Eelative  Fire-risk  of  Oil  Transformers  and  Air- 
Blast  Transformers.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  23,  p.  171.) 

W.  S.  MOODY. — Terminals  and  Bushings  for  High-pressure  Trans- 
formers. (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  23,  p.  225.) 

J.  S.  PECK.— The  Use  of  Ground  Shields  in  Transformers.  (Trans.  Am. 
Inst.  Elec.  Engrs.,  Vol.  23,  p.  553.) 

1906.       . 

DR.  D.  K.  MORRIS  AND  G.  A.  LISTER. — The  Testing  of  Transformers 
and  Transformer  Iron.  (Journ.  Inst.  Elec.  Engrs.,  Vol.  37,  p.  264.) 

K.  L.  CURTIS.— The  Current  Transformer.  (Trans.  Am.  Inst.  Elec. 
Engrs.,  Vol.  25,  p.  715.) 

1907. 

J.  EPSTEIN. — Testing  of  Electric  Machinery  and  of  Materials  for  Its 
Construction.  (Journ.  Inst.  Elec.  Engrs.,  Vol.  38,  p.  28.) 

H.  BOHLE. — Modern  Transformer  Design.  (Journ.  Inst.  Elec.  Engrs., 
Vol.  38,  p.  590.) 

H.  W.  TOBEY.— Eelative  Merits  of  Three-Phase  and  One-Phase  Trans- 
formers. (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  26,  Part  1,  p.  813.) 

J.  S.  PECK. — Eelative  Advantages  of  One-Phase  and  Three-Phase 
Transformers.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  26,  Part  1,  p.  817.) 

C.  C.  CHESNEY.— Forced  Oil  and  Forced  Water  Circulation  for  Cooling 
Oil-insulated  Transformers.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  26, 
Part  1,  p.  835.) 


14     THE    DESIGN   OF   STATIC   TRANSFORMERS 

S.  M.  KINTNER. — Choke-Coils  versus  Extra  Insulation  on  the  End- 
windings  of  Transformers.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  26, 
Part  2,  p.  1169.) 

W.  S.  MOODY. — Protection  of  the  Internal  Insulation  of  a  Static 
Transformer  against  High-frequency  Strains.  (Trans.  Am.  Inst.  Elec. 
Engrs.,  Vol.  26,  Part  2,  p.  1169.) 

H.  W.  TOBEY.— Notes  on  Transformer  Testing.  (Trans.  Am.  Inst. 
Elec.  Engrs,,  Vol.  26,  Part  2,  p.  1169.) 

1908. 

DR.  E.  GOLD  SCHMIDT. — Standard  Performances  of  Electrical  Machinery. 
(Journ.  Inst.  Elec.  Engrs.,  Vol.  40,  p.  455.) 

DR.  H.  BOHLE. — "  Magnetic  Eeluctance  of  Air  Joints  in  Transformer 
Iron.  (Journ.  Inst.  Elec.  Engrs.,  Vol.  41,  p.  527.) 

A.  P.  M.  FLEMING  AND  K.  M.  FAYE-HANSEN. — Transformers  :  Some 
Theoretical  and  Practical  Considerations.  (Journ.  Inst.  Elec.  Engrs., 
Vol.  42,  p.  373.) 

1909. 

E.  G.  EEED. — Transformers.  (Eeport  of  32nd  Annual  Convention  of 
the  National  Electric  Light  Association,  held  at  Atlantic  City  in  June, 
1909,  Vol.  1,  p.  581.) 

A.  B.  EEYNDERS. — Condenser  Type  of  Insulation  for  High-tension 
terminals.  (Trans.  Am.  Inst,  Elec.  Engrs.,  Vol.  28,  Part  1,  p.  209.) 

K.  C.  EANDALL. — High-voltage  Transformers  and  Protective  and  Con- 
rolling  Apparatus  for  Outdoor  Installations.  (Trans.  Am.  Inst.  Elec. 
Engrs.,  Vol.  28,  Part  1,  p.  189.) 

L.  W.  CHUBB. — Method  of  Treating  Transformer  Core  Losses  giving 
Sine-wave  Eesults  on  Commercial  Circuits.  (Trans.  Am.  Inst.  Elec. 
Engrs.,  Vol.  28,  Part  1,  p.  432.) 

LLOYD  AND  FISHER. — The  Testing  of  Transformer  Steel.  (Trans.  Am. 
Inst.  Elec.  Engrs.,  Vol.  28,  Part  1,  p.  439.) 

MOODY  AND  FACCIOLI. — Corona  Phenomena  in  Air  and  Oil  and  Their 
Eelation  to  Transformer  Design.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  28, 
Part  2.,  p.  769.) 

L.  T.  EOBINSON. — Electrical  Measurements  on  Circuits  Eequiring 
Current  and  Potential  Transformers.  (Trans.  Am.  Inst.  Elec.  Engrs., 
Vol.  28,  Part  2,  p.  1005.) 

HILLEBRAND  AND  CHARTERS. — Some  Phases  of  Transformer  Eegula- 
tion.  (Trans.  Am.  Inst.  Elec.  Engrs.,  Vol.  28,  Part  2,  p.  1253.) 

1910. 

MARCHANT  AND  WATSON. — High-tension  Transmission  on  Overhead 
Lines.  (Journ.  Inst.  Elec.  Engrs.,  Vol.  44,  p.  423.) 

E.  D.  GIFFORD. — The  Influence  of  the  Cooling  Media  upon  the  Eise  in 
Temperature  of  Soft  Iron  Stampings.  (Journ.  Inst.  Elec.  Engrs., 
Vol.  44,  p.  753.) 


INTKODUCTOBY  15 

DIGBY  AND  MELLIS. — Physical  Properties  of  Switch  and  Transformer 
Oils.  (Journ.  Inst.  Elec.  Engrs.,  Vol.  45,  p.  165.) 

A.  P.  YOUNG. — Current  Transformers.  (Journ.  Inst.  Elec.  Engrs., 
Yol.  45,  p.  670.) 

J.  J.  FRANK. — Observation  of  Harmonics  in  Current  and  in  Yoltage 
Wave  Shapes  of  Transformers.  (Proc.  Am.  Inst.  Elec.  Engrs.,  Yol.  29, 
Number  5,  p.  665.) 

ADOLPH  SHANE. — Determination  of  Transformer  Eegulation  under 
Load  and  Some  Resulting  Investigations.  (Proc.  Am.  Inst.  Elec.  Engrs., 
Yol.  29,  Number  7,  p.  1089.) 

H.  W.  TOBEY.— Dielectric  Strength  of  Oil.  (Proc.  Am.  Inst.  Elec. 
Engrs.,  Yol.  29,  Number  7,  p.  1171.) 

F.  C.  GREEN. — Problems  in  the  Operation  of  Transformers.  (Proc. 
Am.  Inst.  Elec.  Engrs.,  Yol.  29,  Number  12,  p.  1919.) 

191L 

HARRIS  J.  EYAN. — Open  Atmosphere  and  Dry  Transformer  Oil  as 
High- voltage  Insulators.  (Proc.  Am.  Inst.  Elec.  Engrs.,  Yol.  30, 
Number  1,  p.  1.) 

J.  M.  WEED. — Temperature  Gradient  in  Oil-immersed  Transformers. 
(Proc.  Am.  Inst.  Elec.  Engrs.,  Yol.  30,  Number  1,  p.  119.) 

W.  J.  WOOLDRIDGE.— Hysteresis  and  Eddy  Current  Exponents  for 
Silicon  Steel.  (Proc.  Am.  Inst.  Elec.  Engrs.,  Yol.  30,  Number  1,  p.  139.) 

H.  E.  WILSON. — Commercial  Problems  of  Transformer  Design.  (Proc. 
Am.  Inst.  Elec.  Engrs.,  Yol.  30,  Number  1,  p.  143.) 


CHAPTEE    II 

THE     LEADING     DIMENSIONS      OF     A     TRANSFORMER     OF     A     GIVEN 

RATING 

A  NUMBER  of  papers  have  been  contributed  to  the  proceed- 
ings of  scientific  societies  and  to  technical  periodicals,  dealing 
with  methods  of  determining  upon  the  leading  dimensions 
when  embarking  upon  a  transformer  design.  Most  of  these 
papers,  however,  are  overweighted  with  complex  formula  and 
are  useless  to  the  practical  designer.  In  the  majority  of 
technical  colleges  the  students  investigate  many  interesting 
phenomena  concerning  the  transformer,  but  it  is  rare  to  find 
a  graduate  who  has  the  remotest  idea  of  how  to  proceed  in 
designing  a  commercial  transformer.  This,  of  course,  cannot 
be  due  to  any  real  difficulties  associated  with  transformer 
designing ;  nothing  is  more  simple  and  straightforward  so  far 
as  relates  to  the  underlying  principles.  Nevertheless,  like  all 
designing  problems,  there  are  very  many  practical  points  based 
on  long  experience  to  which  careful  consideration  must  be 
given.  It  is  particularly  true  of  transformer  designing  that 
past  experience  goes  a  long  way  in  aiding  the  engineer  in  the 
case  of  any  particular  new  design  which  he  undertakes.  It  is 
the  object  of  the  present  chapter  to  set  forth  correct  (though 
simple)  preliminary  methods  for  guidance  in  the  commercial 
designing  of  transformers  which  are  required  to  conform  to 
stipulated  conditions.  Various  data,  curves  and  rules  will  be 
introduced  from  time  to  time  to  aid  in  carrying  on  the  design 
at  those  points  where  it  is  necessary  to  make  assumptions. 
The  data  thus  introduced  are  based  on  my  experience  as 
applied  to  a  large  number  of  designs  of  various  ratings.  So  far 


DIMENSIONS  OF  A  TRANSFORMER 


17 


as  it  has  been  practic- 
able to  reduce  this  data 
to  rules,  this  has  been 
done. 

One  cannot  but  feel 
that  the  study  of  trans- 
former design  has 
been  considerably  neg- 
lected in  favour  of  the 
study  of  the  design  of 
other  kinds  of  electri- 
cal machinery.  This 
is  to  be  regretted,  since 
transformers  consti- 
tute by  no  means  a 
minor  detail  in  electri- 
cal engineering  work, 
and  it  is  important  that 
they  should  be  well 
designed  and  well 
built.  The  number  of 
transformers  in  use  is 
increasing  at  an  enor- 
mous rate.  The  most 
unique  characteristic 
of  electricity  as  distin- 
guished from  other 
forms  of  energy  is  the 
high  efficiency  with 
which  transformations 
may  be  effected.  Since 
in  all  but  the  smallest 
sizes  of  static  trans- 
formers efficiencies  in 


FIG.  1. — Outline    sketch    of    a    representative 
design  of  a  core-type  single-phase  transformer. 


excess  of  90  per  cent,  are  customary,  and  since  in  some  of  the 

S.T.  C 


18     THE   DESIGN   OF   STATIC   TKANSFOKMEKS 

large  transformers  which  are  now  coming  into  use,  efficiencies 
of  from  98  to  99  per  cent,  are  obtained,  there  is  but  little 
incentive,  except  as  regards  capital  cost,  for  refraining  from 
interpolating  transformers  at  convenient  points  in  the  system. 


FIG.  2. — Outline  sketch  of  a  representative  design  of  a  shell-type  single- 
phase  transformer. 

Were  engineers  to  fully  recognise  this  point  they  would  not  be 
so  much  concerned  with  the  relative  advantages  and  disadvan- 
tages of  different  forms  of  electricity,  since  any  particular  kind 
of  electricity  may  be  transformed  into  any  other  kind  and  at  very 
high  efficiency.  Even  when  recourse  to  motor-generators  must 


DIMENSIONS   OF   A  TRANSFORMER  19 

be  made,  the  loss  in  transformation  is  very  low  indeed,  and  with 
the  extension  of  the  term  "  transformer  "  to  comprise  "motor- 
generator,"  there  is  no  reason  why  efforts  to  standardise 
periodicity,  pressure  or  number  of  phases  should  be  pushed 
very  far.  It  is  usually  a  much  better  plan  to  employ  in  each 
particular  case  the  number  of  phases,  the  periodicity  and  the 


FIG.  3.— Outline  sketch  of  a  type  of  transformer  adapted  from  Dr. 
Kittler's  "  Handbuch  der  Elektrotechnik,"  1892. 

pressure  best  adapted  to  the  work  to  be  performed,  and  to 
obtain  electricity  of  the  preferred  kind  by  the  interposition  of 
suitable  transformers.  I  am  certain  that  this  policy  will  be  far 
more  generally  followed  in  the  course  of  a  very  few  years,  and 
that  the  aggregate  capacity  of  the  transformers  and  motor  gene- 
rators absorbed  annually  in  engineering  undertakings  will  be 
many  times  greater  even  than  at  present.  This  absolute 

c  2 


20     THE   DESIGN   OF    STATIC   TRANSFORMERS 

increase  will  not  be  simply  in  proportion  to  the  increased 
annual  turnover  of  electrical  machinery,  but  will  constitute  a 
much  larger  percentage  of  the  total  annual  turnover  than  is 
now  the  case.  Hence  manufacturers  who  refrain  from  taking 
up  the  building  of  transformers  are,  in  my  opinion,  ill-advised, 
since  they  will  not  be  so  well  prepared  to  participate  in  the 
increasing  turnover  in  electrical  machinery. 

The  Relative  Merits  of  Various  Types  of  Transformers. 

The  two  main  types  of  transformers  are  the  core  type  and  the 
shell  type.  The  iron  circuit  of  the  former  is  composed  of  a 
rectangular  frame,  upon  the  vertical  legs  of  which  the  primary 
and  secondary  windings  are  placed.  In  the  shell  type  of  trans- 
former the  windings  interchange  places  with  the  iron  magnetic 
circuit  of  the  core  type,  and  the  magnetic  circuit  is  built  around 
the  two  vertical  sides  of  the  more  or  less  rectangular-shaped 
windings.  It  will  thus  be  seen  that,  as  regards  mechanical 
construction,  the  characteristics  of  the  two  types  are  precisely 
reversed.  In  the  core  type  the  copper  windings  envelope  a 
considerable  portion  of  the  magnetic  circuit,  while  in  the  shell 
type  the  magnetic  circuit  envelopes  a  considerable  portion  of 
the  copper  windings.  Practically  the  entire  surface  of  the 
windings  of  the  core  type  are  exposed  to  the  surrounding 
medium  (either  air  or  oil),  while  in  the  shell  type  a  very  large 
portion  of  the  surface  of  the  core  is  thus  exposed. 

In  Fig.  1  is  shown  an  outline  sketch  of  a  representative 
design  for  a  core-type  transformer.  In  this  type  it  will  be  seen 
that  the  two  long  parallel  legs  of  the  rectangular  magnetic 
circuit  carry  the  primary  and  secondary  windings,  the  latter 
generally  being  next  the  core.  A  representative  design  for  a 
shell-type  transformer  is  shown  diagrammatically  in  Fig.  2. 
Another  type,  illustrated  in  Fig.  3  and  adapted  from  an  illus- 
tration in  Kittler's  "  Handbuch  der  Electrotechnik  "  (1892), 
may  be  designated  the  "  circular-shell  type."  The  arrange- 


DIMENSIONS   OF   A  TEANSFOEMEE 


21 


ment  indicated  in  Fig.  3  is  the  predecessor  of  a  type  which  has 

been  put  forward  on  various  occasions,  and,  like  most  types, 

has  its  characteristic  advantages  and  disadvantages.   A  modern 

development   of  the  "  circular-shell "  type   is  known   as  the 

"  Berry  "  transformer,  and  is  shown  diagrammatically  in  Fig.  4. 

The  ''Berry"   type  is  quite  similar  to  Fig.  3  as  regards  the 

disposition  of  the   magnetic    circuit  and  of  the  primary  and 

secondary     windings ;    but    the 

construction  of  the  iron  portion 

is  different,  in  that  it  is  made  up 

of  a  number  of  distinct  groups 

of  core  plates.     The   "  Berry " 

type  is  thoroughly  discussed  by 

Mr.  A.  F.  Berry  in  Vol.  II.  of 

"  Modern  Electric  Practice." 
Much  of  a  controversial  nature 

has  been  written  regarding  the 
relative  merits  of  the  two  main 
types  of  transformers,  namely, 
the  core  type  and  the  shell  type, 
and  the  now-generally-accepted 
conclusion  is,  that,  so  far  as 
electrical  design  is  concerned, 
there  is  very  little  to  choose 
between  the  two  types.  It  is, 
however,  interesting  to  note 
that  the  shell  type  is  rarely 
manufactured  except  by  the  firms  who  took  it  up  many  years 
ago,  and  who  have  been  making  it  ever  since,  and  that  those 
manufacturers  who  have  only  recently  embarked  upon  trans- 
former-building have,  in  nearly  every  instance,  decided  in  favour 
of  the  core  type.  Even  those  manufacturers  who  adopt  the 
shell  type  for  single-phase  transformers  nevertheless  build 
their  three-phase  transformers  of  the  core  type.  In  fact, 
the  core  type  is  pre-eminently  more  suitable  for  three-phase 


FIG.   4. — Diagrammatic  sketch  of 
"  Berry  "  transformer. 


22      THE    DESIGN   OF    STATIC   TKANSFORMEKS 

transformers.     In    Fig.    5    is   shown   a  core-type   three-phase 
transformer,   and  in  Fig.   6   a  shell-type  single-phase  trans- 


former.     These  transformers  \vere  hoth  built  \)y  the  Westing- 
house  Company. 

The  absence  of  radical  advantage  in  any  one  type  as  regards 


DIMENSIONS    OF   A   TBANSFOKMER 


23 


FIG.  6. — 100-kva  single-phase  100  000-volt  shell-type  transformer  built  by  the 
Westinghouse  Co.  for  the  Southern  Power  Co. 


21     THE   DESIGN   OF   STATIC   TRANSFOKMEBS 

electrical  design  has  been  shown  by  A.  P.  M.  Fleming  and 
Faye-Hansen1  in  a  paper  recently  read  before  the  Institution 
of  Electrical  Engineers. 


ILLUSTRATIVE  EXAMPLE  IN  TRANSFORMER  DESIGN. 

For  the  purpose  of  explaining  designing  principles  I  propose 
to  make  calculations  for  a  single-phase  50-cycle  transformer  of 
the  rectangular-core  type  for  a  rated  output  of  20  kilovolt- 
amperes.  I  shall  work  out  the  design  for  a  primary  pressure  of 
5000  volts  and  for  a  secondary  pressure  of  200  volts.  Let  it  be 
required  that  the  regulation  at  full  load  shall  be  within  2,0  per 
cent.  The  transformer  is  to  be  designed  for  use  on  circuits  having 
a  periodicity  of  50  c}Tcles  per  second,  and  supplies  a  load  con- 
sisting exclusively  of  incandescent  lamps.  Consequently  the 
power  factor  of  the  load  is  1,00,  and  the  output  of  the  trans- 
former is  in  this  instance  not  only  20  kilovoltamperes,  but  also 
20  kw.  Let  us  denote  the  power  factor  by  G.  Thus  we  have 
G  =  1,00.  When  the  nature  of  the  load  to  be  put  on  the  trans- 
former is  not  stated  or  known,  it  is  safer,  in  order  to  prevent  mis- 
understanding between  the  customer  and  the  manufacturer,  to 
rate  the  transformer  in  kilovoltamperes.  If,  however,  it  were 
known  that  the  power  factor  would  be,  say,  0,80  and  the  output 
20  kw.,  then  the  transformer  must  be  designed  for  a  current 

corresponding  to  an  output  of  (^TOT;  =)  25  kilovoltamperes. 

\UjOU       / 

From  the  curves  in  Fig.  7  a  rough  preliminary  estimate  of 
the  full-load  efficiency  for  the  transformer  to  be  calculated, 
may  be  obtained.  These  curves  may  in  a  general  way  be  taken 
as  representative  for  all  types  of  single -phase  oil-cooled  trans- 
formers up  to  the  outputs  shown,  whether  of  the  shell  type  or 
of  the  core  type,  and,  in  fact,  no  error  of  consequence  will  be 


1  "  Transformers  :— Some  Theoretical  and  Practical  Considerations,"  A.  P.  M. 
Fleming  and  K.  M.  Faye-Hansen,  Jour.I.E.E.,  Vol.  XLII.,  p.  373. 


DIMENSIONS   OF   A   TKANSFOEMER 


25 


51 


$ 


R 


howing 


Fig. 


introduced  by  embarking   upon  the  calculation  of  natural  air- 
cooled  transformers  on  the  basis  of  these  preliminary  efficiencies. 


26      THE   DESIGN   OF    STATIC   TBANSFOKMEKS 

Few  transformers  of  the  natural  air-cooled  type  are,  however, 
built  nowadays  for  so  large  an  output  as  that  in  question, 
namely,  20  kva.  From  Fig.  7  we  find  that  the  full-load 
efficiency  will  be  of  the  order  of  97,1  per  cent.  In  the  final 
design  it  may  be  found  that  the  calculated  efficiency  does  not 
agree  absolutely  with  that  assumed  from  Fig.  7.  No  radical 
change  will  have  to  be  introduced  in  the  calculations  on  this 
account.  It  will  only  be  necessary  to  make  a  slight  alteration 
in  the  current  so  that  it  shall  correspond  with  the  true  efficiency 
and  also  to  alter  the  factors  dependent  upon  the  current. 
The  primary  current  at  rated  load  is 

20  000 

=  4,12  amperes, 


5000  X  0,971 
and  the  corresponding  secondary  current  is 

20  000 


200 


=  100  amperes.1 


At  the  next  step  a  factor  is  introduced  and  considered  wherein 
large  differences  may  exist,  even  in  equally  good  designs. 
This  factor  is  the  "  volts  per  turn."  In  general,  the  pressure 
between  each  turn  of  the  winding  may  be  varied  over  a  very 
wide  range,  depending  partly  upon  the  object  which  the  designer 
has  in  view,  but  more  especially  upon  the  instinct,  preferences 
and  experience  of  the  individual  designer.  In  designs  for 
fairly  large  outputs,  say,  up  to  300  or  400  kva,  and  for 
high  pressures,  the  determining  factor  for  this  quantity 
(the  "  volts  per  turn  ")  is  the  permissible  pressure,  in  volts, 
which  can,  with  a  sufficiently  large  factor  of  safety,  and  with  due 
regard  to  economy  in  the  space  factor,  be  allowed  between 
each  turn  of  the  windings.  This,  of  course,  applies  to  both 
primary  and  secondary  windings,  since  the  pressure  per  turn 

1  Strictly  speaking,  the  secondary  current  at  rated  load  would  be  100  amperes 
only  if  the  transformer  were  wound  to  give  a  terminal  pressure  of  200  volts  at 
its  rated  load.  Usually,  the  secondary  pressure  ascribed  to  a  transformer  is 
that  at  no  load. 


DIMENSIONS   OF   A   TRANSFORMER 


27 


tfi 

^ 


R 


55 


5} 


I 


I 


1 


flQ 


j   i 


so 

o 
•S 


Q 


is  the  same  in  either.     Another  quantity,  the  "  volts  per  layer," 
although  not  directly  influencing  the  number  of  turns  selected, 


28     THE   DESIGN   OF   STATIC   TRANSFOBMEBS 

does,  to  a  very  considerable  extent,  limit  the  choice  of 
dimensions  and  arrangement  of  the  primary  coils.  In  general, 
the  value  of  the  "  volts  per  layer  "  does  not  affect  the  dimen- 
sions and  arrangements  of  the  secondary  conductors,  especially 


7.0 


0.0 


50 


J 


zo 


/.o 


7 


// 


2O 


/oo 


FIG.  9. — Curves  showing  "  volts  per  turn  "  of  single-phase 
.  transformers  of  different  rated  outputs  and  periodicities. 
Curve  A,  50  cycles  ;  curve  B,  25  cycles. 

where  the  secondary  pressure  is  low.  This  is  for  reasons 
which  will  be  more  apparent  at  a  later  stage  in  the  working- 
out  of  the  design.  In  transformers  of  low  and  of  moderate 
capacity,  the  range  of  suitable  values  for  the  "  volts  per  turn  " 
is  limited  by  other  reasons,  the  chief  of  which  is  the  necessity 


DIMENSIONS   OF   A   TRANSFORMER  29 

for  a  large  number  of  turns  in  order  to  obtain  sufficiently 
small  weights  of  steel  and  sufficiently  low  core  losses.  Thus 
the  values  are  lower  than  would  be  the  case  were  insulation 
safety  factors  the  only  consideration,  and  this  accounts  for  the 
steepness  at  the  start  of  the  curves  in  Fig,  8,  which  show 
graphically  the  relation  between  the  rating,  pressure,  periodicity 
and  "  volts  per  turn  "  obtained  by  an  analysis  of  a  large  number 
of  successful  modern  designs  of  the  core  type.  For  shell-type 
transformers  the  values  shown  may  be  increased  by  some  10  to 
20  per  cent.  It  should  be  mentioned  that  these  curves  are 
plotted  from  designs  proportioned  in  accordance  with  my  own 
practice.  A  good  many  other  designers  prefer  to  employ  a 
less  number  of  turns  and  consequently  higher  values  than  those 
given  in  Fig.  8  for  the  "  volts  per  turn,"  and  although  there 
are  certain  advantages  attending  such  proportions,  yet  it  may 
occur  that  other  (very  often  essential)  qualities  are  sacrificed 
by  their  employment.  Each  designer  will,  as  he  gains  in 
experience,  readily  decide  for  himself  in  each  case  which  of 
these  two  tendencies  he  considers  it  best  to  follow;  but  the  reader 
may  prefer,  until  he  has  obtained  his  own  experience,  to 
employ  the  curves  of  Fig.  9,  which,  while  lying  much  higher 
than  my  usual  values,  are  also  much  below  values  often 
emphtyed  by  some  designers.  It  may  be  remarked  that  for 
veiy  large  transformers  of  several  thousands  of  kilowatts 
capacity,  the  "  volts  per  turn  "  assume  much  larger  values 
than  any  of  those  indicated  in  the  curves.  In  these  very  large 
transformers  the  conductors  are  composed  of  strips.  A  circular 
conductor,  to  give  so  large  a  section,  would  lead  to  a  prohibitive 
amount  of  lost  space  in  winding  the  coils.  These  strips  are 
usually  insulated  by  hand  simultaneously  with  the  process  of 
winding  the  coils.  It  is  thus  possible  to  insulate  the  conductor 
to  any  degree  required  to  ensure  an  ample  margin  of  safety 
with  the  higher  values  of  the  "  volts  per  turn."  Some  appro- 
priate values  for  the  "volts  per  turn  "  for  these  large  transformers 
may  be  taken  from  Table  1. 


30      THE   DESIGN   OF    STATIC   TEANSFOEMEES 

TABLE  1. — VALUES  FOR  "VOLTS  PEE  TURN"  IN  TRANSFORMERS 
OF  LARGE  OUTPUTS. 


Rated  output  in  kva. 

Volts  per  turn. 

500 

13 

1000 

18 

1500 

24 

2000 

30 

2500 

35 

3000 

40 

4000 

52 

5000 

65 

For  our  present  purpose,  let  us  take  for  the  "  volts  per  turn" 
of  the  20-kw  transformer  the  value  read  from  the  curves  in  Fig.  S, 
namely,  1,6  volts.  There  will  thus  be  required  (roughly)  some 

/200       \ 

[ys  =)  125  secondary  turns,  and  3125   primary  turns,  the 

ratio  of  transformation  being  25.  It  is  generally  convenient,  in 
the  first  place,  to  adjust  the  number  of  secondary  turns  to  a 
figure  which  is ;  some  multiple  of  four  or  else  a  multiple  of  some 
even  number  greater  than  four.  Consequently  we  shall  take 
124  secondary  turns  and  (25  X  124  =)  3100  primary  turns. 

Let  us  now  turn  our  attention  to  the  consideration  of  the 
fundamental  orthodox  formula  connecting  the  pressure  with 
the  number  of  turns,  the  periodicity  and  the  total  flux  in  the 
core.  I  consider  that  the  most  useful  way  of  expressing  this 
formula  when  used  for  transformer  design  is 

V  =  0,0444  Too  M 

where  V  represents  the  pressure  in  volts,  T  the  total  number 
of  turns  in  series  between  the  terminals  which  have  a  pressure 
of  V  volts  between  them,  M  the  total  flux  in  megalines  and  <x> 
the  periodicity  of  reversal  of  the  pressure,  in  cycles  per  second. 
This  formula,  'however,  is  only  correct  for  a  transformer 
operated  from  a  circuit  in  which  the  pressure  wave  is  a  sine 
curve,  and  although,  in  many  cases,  it  is  justifiable  to  make 


DIMENSIONS   OF   A   TEANSFOEMEE  31 

the  sinusoidal  assumption  for  approximate  calculations,  there 
is,  in  practice,  often  need  for  greater  accuracy.  The  sine-wave 
assumption  may  in  many  instances  involve  an  error  of  10  per 
cent,  or  more,  in  calculations  relating  to  alternating  electricity 
apparatus.  In  the  case  of  transformers,  the  relation  between 
the  pressure  and  the  flux  is  dependent  upon  the  wave  form  of  the 
pressure,  and  determinations  of  these  quantities  involve  the 
use  of  the  "form  factor"1  of  the  curve.  The  "form  factor" 
of  a  curve  may  be  denned  as  the  ratio  of  the  square  root  of  the 
mean  of  the  squares  (rms)  of  the  ordinates  of  the  curve,  to  the 
mean  value  of  the  ordinates.  Thus,  if  we  denote  the  form 
factor  by/,  we  have 

rms  value  of  ordinates 
*  '"  mean  value  of  ordinates* 

For  the  case  of  a  rectangular  wave,  as  obtained  approximately 
in  the  winding  of  the  armature  of  any  ordinary  generator  of 
continuous  electricity,  the  rms  value  and  the  mean  value  are 
equal  to  one  another,  each  being  equal  to  the  crest  value  of  the 
curve.  The  form  factor  thus  becomes  equal  to  unity,  and  this 
is  the  minimum  possible  value  which  it  can  have.  In  an 
ordinary  continuous-electricity  machine,  however,  the  equation 
connecting  pressure  and  flux  is 

V  =  0,040  T  «>  M 

and  thus  the  equivalent  equation  for  any  other  form  of  curve 
having  a  form  factor  "/"  may  be  written 

V=  0,040/r'co  M.- 
It will  be  seen  that  "  peaked  "  curves  have  high  "  form  factors  " 
and    "flat"    curves   have    low    "form    factors"    when     the 
terms  "  peaked"  and  "flat  "are  taken  to  represent  the  relative 
forms  of  the  pressure  curves,  when  taken  in  conjunction  with 

1  This  term  was  proposed    By   Prof.   Fleming   (see    "Alternating-current, 
Transformers,"  Vol.  L;  2nd  ed.,  p.  583.)- 


32     THE   DESIGN   OF    STATIC   TKANSFOBMEBS 

a  sine  wave  (which  has  a  form  factor  of  1,11).  The  effect  of 
assuming  a  sine-wave  curve  when  the  curve  will  actually  be 
peaked  will  usually  not  be  detrimental  in  any  respect  as 
regards  the  performance  of  the  transformer.  In  fact,  it  can 
easily  be  seen  from  the  precise  formula  given  above,  i.e.,  that 
involving  the  use  of  the  form  factor,  that  the  flux  will  be 
decreased  in  proportion  to  the  "  peakedness  "  of  the  pressure 
curve  and  consequently  the  core  loss  will  also  be  decreased. 
If  the  transformer  is  designed  for  a  high  saturation  of  the  core 
whilst  assuming  a  sine-wave  function,  then  this  decrease  in 
the  core  loss  may  be  quite  considerable  if  the  transformer  is 
operated  on  a  peaked  pressure-curve. 

The  introduction  of  the  form  factor  in  the  flux  formula, 
however,  is  very  necessary  when  the  pressure  curve  is  flat,  in 
order  that  misunderstandings  shall  not  arise  between  the 
buyer  and  the  manufacturer  should  the  core  loss  not  corres- 
pond with  the  specification.  In  any  case,  it  would  be  wise  to 
make  more  conservative  calculations  for  circuits  supplying  flat 
curves  than  for  circuits  supplying  peaked  curves.  It  may  be 
said,  however,  that  there  are  few  instances  in  modern  generat- 
ing plants  where  flat  wave  forms  for  the  pressure  curves  are 
obtained  from  an  alternator,  the  wave  (in  cases  where  there  is 
any  departure  from  the  sine  form)  usually  being  more  or  less 
peaked.  The  modern  tendency  is  strongly  in  the  direction  of 
specifjdng  that  generators  shall  provide  a  sine-wave  curve  of 
pressure  at  all  loads.  The  extent  of  the  dependence  of  the 
form  factor  upon  the  proportions  and  winding  of  an  alternator 
is  fully  discussed  at  p.  92  of  Parshall  and  Hobart's  "  Electric 
Machine  Design  "  ("  Engineering,"  London). 

There  can  be  no  object  gained  by  taking  the  form  factor  into 
account  in  a  design  such  as  that  with  which  we  are  at  present 
dealing,  since  the  application  of  the  form  factor  to  the  calcula- 
tions is  of  the  simplest  nature,  and,  therefore,  having  no 
particular  supply  circuit  in  mind,  we  have  no  reason  for 
assuming  other  than  a  sinusoidal  pressure.  Applying  those 


DIMENSIONS   OF   A   TRANSFORMER  33 

particulars  of  the  design  at  which  we  have  already  arrived,  to 

the  formula 

V  =  0,0444  T  <*>  M 
we  have : 

5000  =  0,0444  X  3100  X  50  X  AT. 

Solving  for  M,  we  find  that  the  total  flux  required  is  equal  to 
0,73  megaline.  In  selecting  the  value  of  the  density  at  which 
to  run  the  core,  one  must  be  guided  to  a  large  extent  by  the 
permeability,  and  by  the  loss  per  unit  of  weight  corresponding 
to  the  grade  of  laminations  which  will  be  employed  in 
constructing  the  core. 

During  the  last  few  years,  there  have  been  placed  on  the 
market  by  various  manufacturers,  brands  of  material  for  trans- 
former cores  which  are  greatly  superior  to  the  brands  formerly 
employed.  It  is  true  that  the  price  of  this  material,  which  may 
be  termed  "  alloyed  steel,"  is  relatively  high,  being  at  present 
some  £30  per  ton  as  against  some  d£13  per  ton  for  the  less- 
suitable  material  formerly  employed.  The  supreme  import- 
ance, however,  of  obtaining  a  minimum  core  loss,  renders  the 
use  of  the  more  costly  material  absolutely  imperative,  and  this 
is  now  conceded  by  most  manufacturers  of  transformers.  As 
regards  permeability,  the  material  is,  on  the  whole,  usually 
inferior  to  the  older  varieties  of  transformer  plates,  but  the 
difference  in  this  respect  is  not  very  pronounced.  The 
saturation  curve  in  Fig.  10  is  based  on  sufficiently  conserva- 
tive permeability  values  to  allow  for  reasonable  deviations 
from  normal  good  quality.  It  is  by  no  means  exceptional 
to  obtain  material,  not  only  in  samples  but  in  bulk,  which 
shows  distinctly  higher  permeability  than  is  indicated  by 
the  standard  curve  in  Fig.  10,  but  it  is  unwise  to  base 
designs  on  the  better  values  obtainable,  unless  the  material 
is  thoroughly  tested  before  acceptance.  Very  slight  varia- 
tions in  the  composition  of  the  material  are  apt  to  be 
accompanied  by  disproportionate  variations  in  the  perme- 
ability. To  the  transformer  manufacturer,  however,  tests  with 
respect  to  permeability  are  of  less  importance  than  is  the  case 

S.T.  D 


34     THE   DESIGN   OF    STATIC   TRANSFORMERS 

with  manufacturers  of  dynamos  and  motors,  since  high  perme- 
ability is  of  much  less  importance  in  the  case  of  transformers 
owing  to  the  relatively  low  densities  at  which  the  cores  are 
usually  worked.  Transformers  for  use  on  circuits  of  very  low 


/O  /$  20  £55  30  35-  40 

/impere  Turns  tier  Cm  of  LengCn  of  (/ore 
FIG.  10. — Saturation  curve  of  representative  sheet  steel. 

periodicity  constitute  an  important  exception  to  this  gene- 
ralisation, and  the  material  for  such  transformers  should  he 
carefully  specified  and  tested  with  respect  to  its  permeability.1 

1  Methods  of  testing  sheet  iron  and  sheet  steel  are  treated  at  considerable 
length  in  Chapter  II.  of  Hobart  and  Ellis  "Armature  Construction" 
(Whittaker  &  Co.,  London).  These  methods  are  as  applicable  to  material 
for  transformers  as  to  armature  laminations. 


DIMENSIONS   OF   A   TRANSFORMER 


35 


It  is  in  the  matter  of  the  loss    accompanying  reversals  of 
magnetisation   that   great     care     must    be    exercised   in   the 


8 
*t 

§^   ^ 

t     5 
\  4. 

*     3 
$     3 

z 


(dOOO         dOOO        /OOOO       /-ZCOO       /-4000 


[FIG.  11.  —  Hysteresis  loss  curve?  for  various  periodicities  for  old  high  loss 

sheet  iron. 


9 
'  8 

7 
^    6 

I  * 

4- 
3 
2 
/ 


6OOO         /OOOO        &OOO      /4OOO 


FIG.  12. — Hysteresis  loss  curves  for  various  periodicities  for  low  loss 
alloy  steel. 

specifying  and  selection  of  the  material  for  transformer  cores. 
This  loss  is  termed  the  core  loss  and  it  has  two  components, 
the  hysteresis  loss  and  the  eddy  loss.  In  the  newer  material 

D2 


36     THE   DESIGN  OF   STATIC   TEANSFOBMEES 


(i.e.,  the  "  alloyed  steel  ")  the  eddy  loss  is  very  nearly  absent ; 
whereas  in  the  formerly- em  ployed  material,  the  eddy  loss  con- 
stituted a  decidedly  substantial  component  of  the  total  core  loss. 
In  fact,  it  is  principally  in  virtue  of  the  very  considerable 


FIG.  13. — Eddy  current  loss  curves  for  various  periodicities  for  old  low 
resistance  sheet  iron. 


£22 


FIG.  14. — Eddy  current  loss  curves  for  various  periodicities  for  modern 
high  resistance  alloy  steel. 

increase  in  the  specific  resistance  of  the  material  and  of  the 
consequent  great  reduction  in  the  eddy  loss  that  the  marked 
decrease  in  the  total  core  loss  has  been  brought  about.  The 
older  material  sometimes  had  a  specific  resistance  as  low  as 
10  microhms  per  centimeter  cube,  whereas  in  the  new 


DIMENSIONS   OF   A   TRANSFORMER 


37 


alleged  steel  this  is  usually    increased  to    45    microhms  per 
centimeter  cube,    and,     in   some    instances,    to    even  higher 


o 


I 


E 


/-40OO 


FIG.  15. — Total  loss  curves  for  various  periodicities  for  old  high  loss 
sheet  iron. 


FIG.  16. — Total  loss  curves  for  various  periodicities  for  low  loss  alloy  steel. 

values.  A  slight  decrease  has,  it  is  true,  also  been  effected 
in  the  hysteresis  component  of  the  total  core  loss,  as  may 
be  seen  by  comparing  the  curves  in  Figs.  11  and  12,  but 


38     THE    DESIGN   OE   STATIC   TRANSFORMERS 


I 


DIMENSIONS   OF   A  TRANSFORMER 


39 


this  decrease  is  small  when  compared  with  the  decrease  in 
the  eddy  loss  revealed  by  contrasting  the  curves  of  Fig.  14 
with  those  of  Fig.  13.  The  resultant  improvement  which 
has  been  effected  may  be  seen  by  comparing  the  total  core 
loss  in  the  new  material,  as  indicated  by  the  full  lines  in 
Fig.  16,  with  the  total  core  loss  in  the  older  variety  as 
indicated  by  the  full  lines  in  Fig.  15.  The  dotted  lines  in 
Figs.  15  and  16  represent  the  hysteresis  component  repro- 
duced from  Figs.  13  and  14,  and  it  is  interesting  to  note 
that  the  hysteresis  component  in  the  case  of  the  new  material, 
is,  at  low  periodicities,  scarcely  distinguished  from  the  total 
core  loss.  This  is  brought  out  still  more  strikingly  by  the 
curves  in  Figs.  17  and  18,  where  the  hysteresis  and  eddy  losses 
are,  both  for  the  old  and  for  the  new  material,  plotted  as  per- 
centages of  the  total  core  loss. 

The  magnetic  densities  which  may  usually  be  emplo3fed 
in  oil-cooled  transformers  consistently  with  obtaining  results 
conforming  with  present-day  standards  are  set  forth  in 
Table  2. 

TABLE    2. — DATA    OF    CORE    DENSITIES    FOE,    USE    AS    PRELIMINARY 
ASSUMPTIONS  IN  THE  DESIGN  OF  OIL-COOLED  TRANSFORMERS. 


Rated 
output  in 
kva. 

25  cycles. 

50  cycles. 

Single-phase. 

Three-phase. 

Single-phase. 

Three-phase. 

Primary  pressure. 

Primary  pressure. 

Primary  pressure. 

Primary  pressure. 

2000 

10000 

2000 

10000 

2000 

10000 

2000 

10  000 

5 

12000 

12  000 

11  500 

11  500 

11  000 

10  500 

10500 

10000 

10 

13000 

12  000 

12000 

12000 

11  200 

11  000 

11000 

10500 

20 

13  500 

13  000 

12  500 

12  500 

11  500 

11  000 

11000 

10  500 

50 

14000 

13  500 

13  500 

13  000 

11  500 

11  200 

11500 

11000 

100 

14  000 

13  500 

14000 

13  500 

11  800 

11  500 

11500 

11000 

40      THE   DESIGN    OF    STATIC   TEANSFOEMERS 

TABLE  3. — CORE  DENSITIES  FOR  USE  AS  PRELIMINARY  ASSUMPTIONS 
IN  THE  DESIGN  OF  NATURAL  AIR-COOLED  AND  OF  AIR-BLAST 
TRANSFORMERS. 


Rated  output  in  kva. 

50-cycle  natural  air-cooled 
transformers. 

50-cycle  air-blast 
transformers. 

5 

9000 

10 

8500 



20 

8000 

—    .  - 

25 

8000 



50 

8000  ) 

12  500 

100 

7500     i 

12200 

200 

7000) 

12000 

300 

— 

11  500 

500 

— 

11  500 

For  air-blast  transformers  or  transformers  of  large  capacities, 
the  values  set  forth  in  Table  3,  will  be  found  more  appropriate. 
These  densities  may  be  departed  from  to  a  considerable  extent 
without  necessarily  sacrificing  the  quality  of  the  designs  ;  and 
this  matter  of  the  selection  of  densities  affords  another  instance 
where  individual  discretion  must  be  applied.  Some  designers 
have  adopted  the  practice,  when  calculating  a  line  of  standard 
transformers,  of  arranging  that  the  density  for  a  given 
periodicity  shall  be  the  same  for  a  large  range  of  capacities ; 
but  such  a  procedure  either  entails  high  no-load  currents  in 
the  small  sizes  or  uneconomical  use  of  the  steel  in  the  larger 
sizes.  It  is  for  this  reason  that  the  values  of  the  core  density 
given  in  Table  2  have  been  adjusted  to  increase  with  increased 
output.  The  lower  values  are  necessary  with  transformers  of 
small  sizes  in  order  to  obtain  suitably-low  values  for  the  no- 
load  current,  while  in  large  transformers  the  no-load  current 
will  not  exceed  permissible  values  even  when  somewhat  higher 
magnetic  densities  are  employed.  These  higher  values  neces- 
sarily involve  more  iron  loss  per  unit  of  weight,  but  the 
increased  losses  may  be  taken  care  of  by  the  cooling  medium, 


1  These  densities  can   only    be    used    where   ample  ventilating    ducts  are 
employee!  in  the  core. 


DIMENSIONS   OF   A  TRANSFORMER  41 

which,  in  the  design  we  are  considering,  is  oil.  With  natural 
air-cooled  transformers  the  magnetic  density  must,  however, 
decrease  with  increase  of  output,  as  shown  in  Table  3,  and  this 
for  the  reason  that  the  output,  and  therefore  (roughly)  the 
aggregate  loss,  varies  as  the  cube  of  the  linear  dimensions, 
whereas  the  cooling  surface  only  varies  as  the  square  of  the 
linear  dimensions.  If,  therefore,  the  same  density  were  used 
for  all  sizes,  the  heating  would  either  be  excessive  with  the 
large  outputs,  or  needlessly  low  with  the  small  outputs.  This 
does  not  apply  (or  at  any  rate,  not  to  so  great  an  extent)  to 
oil-cooled  transformers,  since  the  heating  is  then  no  longer 
exclusively  a  function  of  the  cooling  surface  of  the  transformer 
itself,  but  also  of  the  surface  of  the  containing  case,  and  of  the 
quantity  of  oil  per  kilowatt  of  total  loss.  The  core  density  in 
air-blast  transformers  must  also  decrease  with  increase  of  out- 
put, although  not  to  so  large  an  extent  as  with  natural  air- 
cooled  transformers.  The  reason  of  this  will  be  apparent  from 
the  nature  of  the  air-blast  cooling  problem  as  discussed  in 
Chapter  X. 

From  Table  2,  we  find  that  for  our  20-kw  transformer  we 
should  employ  a  core  density  of  11,5  kilolines  per  sq  cm. 
We  have  already  found  that  by  substitution  in  the  formula 
V  =  0,0444  T  co  M,  5000  =  0,0444  X  3100  X  50  X  M,  the 
flux  works  out  at  M  =  0,730  megaline.  Consequently  the 
net  cross-section  of  iron  required  in  the  magnetic  circuit  is 

730  000 


The  core  is  built  up  of  sheets  having  a  thickness  of  0,5  mm. 
These  sheets  are  japanned  on  one  side  so  that  each  shall  be 
insulated  from  its  neighbour,  thus  decreasing  the  eddy  loss  in 
the  core.  It  is,  of  course,  essential  to  provide  some  insulation 
between  the  core  plates,  but  there  are  differences  of  opinion  as 
to  the  preferable  constitution  of  this  insulation.  Paper, 
varnish,  and  a  film  of  oxide  caused  by  annealing,  are  alternatives 


42     THE   DESIGN   OF   STATIC   TRANSFORMERS 

employed  by  different  manufacturers.  While  the  film-of-oxide 
method  leads  to  a  higher  iron  factor,  i.e.,  while  the  loss  of  space 
due  to  insulation  is  less  than  in  either  of  the  other  two  methods, 
it  is  none  too  reliable.  Papering  the  plates  on  one  side  has  been 
asserted  to  be  the  most  reliable  method,  but  it  entails  considerable 
expense  whether  carried  out  by  machinery  or  by  hand.  Paper 
insulation  also  takes  up  somewhat  more  space  than  does  a  film 
of  oxide  or  of  varnish,  and  is  not  likely  to  be  as  permanent  an 
insulation  as  that  provided  by  a  suitable  varnish.  The  paper 
will  ultimately  be  reduced  to  powder  under  the  influence  of  the 
alternate  heating  and  cooling  of  the  core.  In  some  cases  of 
paper-insulated  cores  which  were  taken  apart  after  a  few  years 
of  service,  the  paper  was  found  to  be  in  an  advanced  stage  of 
disintegration,  and  the  laminations  had  become  oxidised  under 
the  influence  of  exposure  to  certain  constituents  of  the  paste 
with  which  the  paper  had  been  applied.  The  danger  of 
disintegration  is,  however,  lessened  in  oil-cooled  transformers 
as  the  oil  tends  to  preserve  the  paper.  The  thickness  of  the 
core  plate  is  determined  upon  from  a  study  of  the  component 
losses.  It  is  evident  from  consideration  of  the  results 
embodied  in  the  curves  of  Figs.  17  and  18  (on  p.  38),  that 
with  the  modern  alloyed  iron,  the  eddy  loss  is  so  exceedingly 
low  that  far  less  advantage  is  obtained  by  employing  thin  sheets 
than  was  the  case  with  the  formerly-used  quality  which,  as  has 
been  pointed  out,  had  very  low  specific  resistance.  Whereas 
with  the  former  material  it  was  important,  in  high-periodicity 
transformers,  to  employ  sheets  of  as  low  a  thickness  as  0,35  mm, 
it  is  my  opinion  that  with  the  newer  material,  whose  specific 
resistance  is  three  times  as  great,  there  is  insufficient  object  in 
employing  a  less  thickness  than  0,50  mm ;  in  fact,  I  should  be 
inclined  to  adopt  this  or  even  a  greater  thickness,  as  a  convenient 
standard  for  transformer  cores.  It  must  be  remembered  that  the 
thicker  the  transformer  plate,  the  less  is  the  percentage  of  space 
occupied  by  the  insulating  varnish  on  the  plate.  Taking 
0,025  mm  as  a  representative  thickness  of  core-plate  varnish, 


DIMENSIONS   OF    A  TRANSFORMER 


43 


the  deductions  which  must  be  made  on  account  of  the  space 
occupied  by  insulation  when  plates  of  different  thickness  are 
employed  are  as  set  forth  in  Table  4. 

TABLE  4. — SPACE  OCCUPIED  BY  INSULATION  ON  TRANSFORMER  CORE 
PLATES  FOR  VARIOUS  THICKNESSES  OF  CORE  PLATES.  (DIMENSIONS 
IN  MM.) 


Thickness  of  bare  lamination. 

0,20 

0,30 

0,40 

0,50 

0,60 

Average  thickness  of  insulation 

per  core  plate    .... 

0,025 

0,025 

0,025 

0,025 

0,025 

Thickness  of  residual  lost  space 

per  core  plate   .... 

0,015 

0,015 

0,015 

0,035 

0,015 

Total   thickness  per    core    plate 
(insulated  and  compressed) 

0,24 

0,34 

0,44 

0,54 

0,64 

Percentage  which  the  iron  cross 

section  constitutes  of  the  gross 

cross  section  of  the  core    . 

83,5 

88,3 

91,0 

92,7 

93,8 

The  values  for  core  plates  as  given  in  Table  4,  as  also 
representative  values  when  oxide  insulation  and  paper  insula- 
tion are  employed,  are  plotted  in  the  three  curves  of  Fig.  19. 
When  the  core  plates  have  a  thickness  of  0,50  mm,  the  japan 
varnish  will,  according  to  the  curve  in  Fig.  19,  only  occupy 
7  per  cent,  of  the  gross  core  length.  Consequently  we  shall  be 
well  on  the  safe  side  in  allowing  10  per  cent.  The  net  core 
length  (An)  should  thus  be  taken  as  0,90  of  the  gross  core 
length  (A$).  Another  consideration  is  that  the  thinner  the 
core  plate,  the  greater  will  be  the  percentage  which  the  skin 
of  inferior  magnetic  quality  bears  to  the  total  thickness  of 
the  lamination,  for  it  is  well-known  that  the  permeability  is 
usually  lower  the  less  the  thickness  of  the  core  plate,  for  any 
given  grade  of  material.  Furthermore  the  costs  of  the  lamina- 
tions themselves,  and  the  outlay  for  the  labour  attending  their 
assembly,  increase  with  decreasing  thickness.  The  most 
usual  thicknesses  of  laminations  used  in  transformer  manu- 
facture vary  between  0,35  mm  and  0,50  mm,  the  latter  or 


44     THE   DESIGN   OF    STATIC   TKANSFOBMEKS 

even    a  still  greater  thickness  being   quite  appropriate    with 
modern  alloyed  steel. 


w 


42 


FIG.  19. — Curves  showing  the  effect  of  various  kinds  of  core  insulation  on  the 
nett  effective  iron  in  transformer  cores  for  various  thicknesses  of  stampings. 

Dipping  tanks  and  drying  ovens  are  essential  adjuncts  to  the 
manufacture  of  transformers,  and  my  opinion  is  that  when  all 
these  facts  are  considered,  it  is  best  practice  to  insulate  the 


DIMENSIONS  OF  A  TRANSFORMER 


45 


laminations  by  varnishing  them,  either  all  of  them  on  one  side, 
or  half  of  them  on  both  sides  (the  remaining  half  being 
left  bare).  The  object  can  best  be  accomplished  by  passing 
the  plates  through  a  pair  of  varnishing  rollers  or  by  dipping  the 
plates  in  varnish  and  then  drying  them  by  passing  them  over 


'onq 


FIGS.  20  and  21.— Types  of  sections  of  transformer  cores. 

gas  jets  or  by  other  heating  arrangements.  Should  such  heating 
not  be  convenient  or  possible,  the  varnish  should  preferably  be 
of  a  variety  which  is  capable  of  drying  in  the  open  air  within 
ten  or  fifteen  minutes. 

For  our  design  we  shall  employ  varnished  laminations  of 
0,50  mm  thickness,  and  thus  the  space  taken  up  by  the  varnish 
will  amount  to  about  10  per  cent,  of  the  gross  cross-section  of 


46     THE   DESIGN  OF   STATIC   TRANSFORMERS 


the  core.     In  order,  therefore,  to  obtain  the  required  section 
of  iron,  the  gross  cross-section  of  the  core  must  be 

C*  O   £5 

=  70,0  sq  cm. 


r 


Cruciform 
FIGS.  22  to  25. — Types  of  sections. of  transformer  cores.. 

The  preferable  shape  of  the  cross- section  is  in  itself  a  ques- 
tion requiring  careful  study.    Some  of  the  various  types  which 


FIG.  26. — Core  section  for  elliptical-shaped  coil. 

have  been  used,  and  some  of  which  are  still  in  common  use, 
are  indicated  in  Figs,  20  to  26.  Figs.  20  and  21  show  the 
square-  and  oblong-sectioned  cores  with  similarly-shaped  coils 


DIMENSIONS   OF  A  TEANSFORMEB 


47 


surrounding  them ;  Figs.  22  to  25  show  circular  coils  surrounding 
variously-shaped  cores,  and  Fig.  26  shows  an  elliptical  coil 
enclosing  a  stepped-cruciform  core.  The  rectangular  (or  square) 


Id 


/O    2O    30     JO    30     60    70    80 

/// 

FIG.  27. —  Curves  showing  the  relation  between  the  output  and  the  width 
of  winding  space. 

type  is  the  simplest  to  build  up,  and  is  the  most  extensively 
used,  whereas  the  polygonal  (Fig.  23),  cruciform  (Fig.  24)  and  an 
extension  of  the  cruciform  which  may  be  termed  the  "  stepped  " 
cruciform  type  (Fig.  25)  are  preferred  by  some  designers.  It  is 
seen  from  Figs.  22  to  25  that  for  circular  coils  it  is  desirable 


48     THE   DESIGN   OF   STATIC    TRANSFORMERS 

to  adopt  the  cruciform  or  stepped  cruciform  core,  in  order  to 
secure  maximum  cross- section  of  iron  with  good  provision  for 
cooling  and  with  short  length  of  mean  turn.  The  polygonal 
core  (Fig.  23)  is  undesirable  on  account  of  the  many  different 
widths  of  the  stampings  required  and  of  the  consequently 
increased  cost  attending  cutting  and  assembling. 

For  our  present  design,  let  us  adopt  the  oblong  shape 
(Fig.  21),  and  without  entering  upon  a  consideration  of  the 
most  economical  dimensions  of  the  rectangle  (as  this  is  purely 
a  matter  of  experience  and  judgment),  let  us  employ  cores 
measuring  7,0  cm  wide  by  10,0  cm  deep. 


FIG.  28. — Section  of  20-kw  5000/200-volt  transformer  core  (dimensions 
in  centimeters). 

In  transformers  of  this  type,  it  is  generally  undesirable  to 
employ  great  depths  of  winding,  and,  bearing  this  consideration 
in  mind,  there  have  been  plotted  in  the  curves  in  Fig.  27 
values  for  the  gross  width  of  the  winding  space,  i.e.,  the  width 
of  the  window,  for  various  outputs  and  periodicities.  These 
curves  may  be  used  for  preliminary  trial  designs.  It  is  by  no 
means  intended  that  these  values  should  be  strictly  adhered  to 
in  the  final  design.  On  the  contrary,  it  is  often  necessary  to 
appreciably  alter  the  width  of  the  winding  window  when  we 
reach  the  point  of  laying  out  the  shapes  of  the  coils  them- 
selves. From  Fig.  27  we  find  that  some  8,5  cm  constitutes  a 
reasonable  trial  value  for  the  width  of  the  winding  window  of 
our  20-kw  transformer. 


DIMENSIONS   OF   A  TKANSFOKMER 


49 


We  now  have  all  the  material  for  sketching  out  a  rough  plan 
of  the  magnetic  circuit.  The  section  is  shown  in  Fig.  28.  In 
Fig.  29  are  indicated  in  plan  the  outlines  of  the  secondary  and 
primary  windings,  from  which  the  mean  lengths  of  the 
secondary  and  primary  turns  may  be  scaled  off.  These  mean 
lengths  of  turn  are  found  to  be  40  cm  and  53  cm  respectively. 

The  reader  will  note  that  the  depth  of  the  secondary  winding 
has  in  Fig.  29  been  taken  at  9  mm,  while  a  depth  of  23  mm. 
has  been  assigned  to  the  primary  winding.  It  is  impracticable 


FIG.  29.— Section  of  winding  and  core  of  a  20-kw  5000/200-volt  transformer 
(dimensions  in  centimeters). 

to  lay  down  rules  to  cover  this  point,  but  in  general,  the 
primary  winding  will  occupy  a  much  greater  depth  than  the 
secondary  winding,  although  for  transformers  with  so  moderate 
a  primary  pressure  as  that  of  the  present  design  the  disparity 
will  not  usually  be  so  great.  The  reason  it  is  so  great  in  this 
instance  is  that,  as  will  be  seen  a  few  pages  later,  the  trans- 
former is  proportioned  for  the  same  P  R  loss  (at  full  load)  in 
the  primary  as  in  the  secondary,  and  since  the  primary  is 
outside  and  has,  consequently,  a  greater  length  of  mean  turn, 
it  is  necessary  to  operate  it  at  a  lower  current  density  (in  order 
S.T.  E 


50     THE   DESIGN   OF   STATIC   TBANSFOBMEBS 

to  bring  about  this  equality  in  the  losses)  than  is  employed  in 
the  secondary*  Of  course,  even  for  the  same  current  density, 
the  section  of  the  primary  coil  will  be  the  greater  because  of 
the  greater  amount  of  space  devoted  to  insulation  between  the 
many  turns  and  many  layers.  In  other  words,  the  cross- 
section  through  the  primary  coil  is,  for  two  reasons,  much 
greater  than  that  through  the  secondary  coil.  The  first  reason 
is  that  in  this  particular  example  the  plan  has  been  followed 
of  having  the  full-load  loss  in  the  primary  coil  equal  to  the  full- 
load  loss  in  the  secondary  coil.  The  second  reason  relates  to 
the  inherently  and  necessarily  lower  utilisation  of  the  space  in 
the  primary  coil  as  compared  with  the  utilisation  of  the  space 
in  the  secondary  coil.  The  second  reason  is  fundamental,  but 
as  to  the  first  reason,  the  transformer  might  equally  well  have 
been  proportioned  for  a  greater  loss  in  the  primary  coil  at  full 
load  than  in  the  secondary  coil.  Had  this  latter  plan  been 
followed,  the  depth  of  the  secondary  winding  would  have  more 
nearly  approached  the  depth  of  the  primary  winding. 

,The  winding  used  (see  Fig.  29)  is  that  known  as  the  simple 
concentric  type,  which  is  the  commonest  form  for  this  t}rpe  of 
transformer.  As  applied  to  a  core-type  transformer,  it  is 
shown  in  plan  and  elevation  in  Fig.  30.  Its  advantages  are 
that  it  gives  a  high  space  factor,  and  at  the  same  time  presents 
a  large  cooling  surface  to  the  action  of  the  cooling  medium, 
thus  enabling  the  copper  to  be  worked  at  comparatively  high 
densities.  To  secure  close  regulation  on  inductive  load,  it  is 
sometimes  necessary  to  adopt  the  triple  concentric  winding 
which  reduces  the  leakage  of  lines  to  well  down  toward  half 
the  value  obtained  with  the  simple  concentric  type.1  A  triple 
concentric  winding  is  shown  diagrammatically  in  Fig.  31. 

An  arrangement  is  shown  in  Fig.  32  which  may  be  termed  a 
sandwich  winding,  and  it  might  at  first  sight  be  supposed  that 
it  would  lead  to  obtaining  still  better  regulation.  This  will  be 

1  For  a  further  discussion  of  this  subject  of  magnetic  leakage  the  reader 
should  consult  Chapter  VII.  on  the  regulation  of  transformers. 


DIMENSIONS   OF   A   TRANSFORMER 


51 


the    case   if  the   intermixing   is   carried   far  enough,  but    in 
Chapter  VIL,  dealing  with  the  regulation  of  transformers,  it 


FIG.  30. — Simple  concentric 
winding. 


FIG.  31. — Triple  concentric 
winding. 


will  be  made  plain  that  there  is  another  consideration  than  that 
of  mere  intermixing,  namely,  the  reluctance  of  the  leakage 
path  between  the  primary  and  secondary  coils.  The  sandwich 

E2 


52     THE   DESIGN   OF   STATIC   TKANSFORMEBS 

winding  as  illustrated  in  Fig.  32  can  be  excellently  arranged 
as  regards  insulation,  and  lends  itself  well  to  the  use  of  form- 
wound  coils.  It  also  affords  maximum  facility  for  the  replace- 


FIG.  32. — Sandwich  winding. 


FlG.  33. — Simple  concentric  winding 
with  subdivided  primary. 


ment  of  damaged  coils.     On  the  other  hand,  unless  carefully 
studied  out,  it  will  have  a  low  "  space  factor." 

In  Fig.  33  is  shown  a  simple  concentric  winding  with  sub- 
divided primary.     The  arrangements  shown  in  Figs.  32  and  33 


DIMENSIONS   OF   A   TRANSFORMER  53 

both  have  an  advantage  in  the  reduced  pressure  per  layer. 
Thus  if,  in  Fig.  33,  the  primary  winding  had  consisted  of  a 
coil  running  the  full  length  of  the  core,  instead  of  heing 
divided  up  into  eight  component  coils,  the  pressure  between 
the  end  turns  of  adjacent  layers  would  have  been  eight  times 
as  great,  and  consequently  more  insulation  between  layers 
would  have  been  required. 

Our  20-kva  transformer  is  to  be  proportioned  for  a  total 
drop  of  2,0  per  cent,  at  full  load  of  unity  power  factor.  If  of 
this  amount  we  arrange  that  some  1,8  per  cent,  shall  constitute 
the  I II  drop  at  rated  load,  then  the  coils  can  be  so  designed 
that  the  inductive  drop  will,  for  a  load  of  unity  power  factor, 
not  increase  the  total  drop  at  rated  load  to  over  the  stipulated 
2,0  per  cent.  The  calculation  of  the  inductive  component  of 
the  total  drop  is  considered  in  Chapter  VII.  It  is  often  desir- 
able to  adhere  to  a  certain  value  of  the  regulation  in  standard 
transformers,  as  it  is  customary  to  operate  considerable 
numbers  of  them  in  parallel  on  the  same  secondary  circuit, 
and  unless  the  regulation  at  rated  load  is  the  same  in  all  of 
them,  they  will  not  share  the  load  in  proportion  to  their  rated 
capacities.  Let  us  divide  the  1,8  per  cent.  I  R  drop  equally 
between  the  primary  and  secondary  windings,  though  this  will 
not  necessarily  lead  to  the  best  design  in  all  cases.  Then  the 
pressure  drop  in  the  primary  winding  will  amount  to  (0,009  X 
5000  =)  45,0  volts,  and  that  in  the  secondary  winding  to 
(0,009  X  200  =)  1,80  volts.  The  primary  and  secondary 
currents  at  full-load  are  respectively  4,12  and  100  amperes. 
The  resistance  of  the  primary  must  therefore  be  equal  to 

g|=  10,9  ohms, 

and  that  of  the  secondary  to 

1   ftO 

if  =  0,018  ol,». 
The  total  length  of  the  primary  winding  is  (3100  X  53  =) 


54      THE   DESIGN   OF    STATIC   TEANSFORMEES 

164  000  cm.     The  section  of  the  primary  winding  to  give  the 
above  resistance  at  60°  C.  must  therefore  equal 

164  000  X  0,0000020 

cm 


10,9 

and  since  the  total  length  of  the  secondary  conductor  is 
(124  X  40  =)  4960  cm,  the  section  of  the  secondary  conductor 
must  equal 

4960  X  0,0000020  __ 
0,018 

The  current  density  at  rated  load  equals 

4  12 

A  '    n  =  137  amperes  per  sq  cm 
U,UoU 

In  the  primary  copper,  and 

0          =  184  amperes  per  sq  cm 

in  the  secondary  copper.  The  difference  in  these  two  densities 
is  due  to  the  plan  adopted  in  this  design,  namely,  that  the 
percentage  pressure  drop  shall  be  the  same  in  the  primary  and 
secondary  windings. 

It  will  be  observed  that  in  our  example  we  have  adopted  a 
method  by  which  the  current  density  has  been  deduced.  There 
are  innumerable  alternative  methods  of  carrying  out  a  set  of 
designing  calculations,  and,  as  a  matter  of  fact,  the  experienced 
designer  employs  sometimes  one  and  sometimes  another, 
according  to  the  way  in  which  each  case  as  it  arises  appeals  to 
him,  or  according  to  his  mood.  Thus  it  is  useful  to  have  at 
hand  rough  representative  values  of  current  densities  which,  in 
this  type  of  design,  are  found  by  experience  to  lead  to  good 
results. 

As  a  matter  of  fact,  however,  widely  different  current 
densities  may  be  emplo}Ted  in  equally  good  designs,  since,  as 
we  shall  see  later,  the  heating  of  an  oil  transformer  is  mainly  a 


DIMENSIONS   OF   A   TRANSFORMER 


55 


question  of  the  loss  per  square  decimeter  of  external  radiating 
surface  of  the  case,  and  is  only  in  a  lesser  degree  dependent 
upon  the  actual  distribution  of  these  losses  in  the  copper  and 
in  the  iron,  or  upon  their  intensity  at  various  parts.  But  for 
the  purpose  of  preliminary  assumptions  there  are  brought 
together  in  Table  5  some  average  data  based  on  the  current 
densities  which  have  been  employed  in  a  large  number  of 
instances  taken  from  good  practice. 


TABLE  5. — MEAN  OF  PRIMARY  AND  SECONDARY  CURRENT  DENSITIES 
IN  TRANSFORMERS  OF  VARIOUS  SIZES  WHEN  OPERATED  AT  THEIR 
BATED  LOADS. 


Rated  output 

25  cycle. 

50  cycle. 

in  kva. 

Single  phase. 

Three  phase. 

Single  phase. 

Three  phase. 

5 

100 

90 

130 

120 

10 

115 

105 

145 

130 

20 

130 

125 

160 

150 

50 

140 

130 

165 

155 

100 

150 

140 

170 

160 

We  have  already  found  that  the  primary  conductor  must 
have  a  cross-section  of  3,0  sq  mm.  Consequently  for  the 
primary  winding  we  shall  employ  a  single-cotton-covered  wire 
with  a  bare  diameter  of 


•j 


4  x  3,0 
3,14 


=  1,96  mm. 


Since  we  have  designed  our  windings  to  have  a  normal  pressure 
of  only  1,6  volts  between  each  turn,  sufficient  insulation  is 
afforded  by  a  single-cotton  covering  on  the  wire.  For  designs 
having  over  4  volts  per  turn,  it  is  usually  advisable  to  employ 


56      THE   DESIGN   OF    STATIC   TRANSFORMERS 


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DIMENSIONS   OF   A  TBANSFOEMEE  57 

double-cotton  coverings.  When  impregnated  with  suitable 
varnishes,  double-cotton  coverings  will  be  quite  reliable  up  to 
some  15  volts  or  more  per  turn.  The  external  diameter  of  a 
single-cotton-covered  wire,  whose  bare  diameter  is  1,96  mm, 
will  be  2,11  mm.  The  secondary  conductors  will  be  made  up 
of  flat  strips  of  a  suitable  section,  the  precise  dimensions  of 
which,  however,  can  >  only  be  definitely  and  conveniently  deter- 
mined at  a  later  stage  of  the  calculations. 

The  total  cross-section  of  the  copper  in  the  winding  space  is 
made  up  as  follows : — 

Primary  copper          3100  X  0,030  =  93,0  sqcm. 

Secondary  copper      ...          ...  124  X  0,545  =  67,5  sqcm. 

Total  section  of  primary  and 

secondary  copper          ...  93  +  67,5     —  160,5  sq  cm. 


This  total  section  of  copper  has  to  be  contained  in  the 
winding  space  or  "  window,"  but  this  does  not  constitute  the 
total  section  of  the  -ivindo-w  since  it  is  desirable  to  employ  air 
spaces  between  the  windings  and  the  core.  The  proportion 
which  the  copper  section  bears  to  the  window  section  is  known 
as  the  "  space  factor,"  and  this  varies  both  with  the  type  of 
core,  the  type  of  winding,  and  with  the  pressure  for  which  the 
coils  are  wound.  Suitable  values  of  the  space  factor  may  be 
obtained  from  the  curves  in  Fig.  34,  which  apply  to  the 
rectangular  core  type.  For  the  cruciform  or  stepped  core  type 
values  corresponding  to  the  curves  in  Fig.  35  may  be  taken  for 
preliminary  assumptions.  It  will  be  observed  that  the  latter 
type,  i.e.,  the  cruciform  core  type,  possesses  a  considerably 
smaller  space  factor  for  a  given  output,  and  the  reason  for 
this  becomes  evident  when  the  winding  arrangement  indicated 
in  Figs.  24  and  25,  on  p.  46,  are  studied.  While  the  inside  coil 
of  the  rectangular  type  is  wound  close  up  against  the  core,  inside 
the  window,  as  shown  in  Fig.  29,  on  p.  49,  the  cruciform  core,  in 


58     THE   DESIGN   OF    STATIC   TRANSFORMERS 


virtue  of  its  symmetrical  nature, 
provides  an  air  duct  between 
the  core  and  the  inside  of  the 
coil.  This  duct  is  included  in 
the  window  section,  and  leads  to 
the  low  space  factors  indicated 
in  Fig.  35. 

From  Fig.  34  we  find  that 
a  space  factor  of  about  0,37 
may  be  obtained  in  a  design 
such  as  that  with  which  we 
jare  dealing.  This  value  will 
afford  a  sufficient  guide  to 
obtaining  the  total  cross- 
section  of  the  winding  window. 
Thus  the  total  required  area 
will  be  some 


161 
0,37 


=  435  sq  cm. 


We  have  already  determined 
the  width  of  the  winding  space 
to  be  about  8,5  cm,  and  there- 
fore the  length  of  the  winding 
space  may  be  estimated  at 


435 

8,5 


=  ol  cm. 


FIG.  36.— Sketch  of  core  for  a  20-kw 
5000/200-volt  50-cycle  transformer. 


The   core   as  thus    determined 
upon  is  drawn  in  Fig.  36. 


CHAPTER    III 

THE    COEE    LOSS    AND    THE    ANNUAL   EFFICIENCY. 

WE  may  now  proceed  with  the  estimation  of  the  core  loss  of 
the  20-kw  transformer  which  we  are  designing.  The  amount 
of  the  core  loss  is  an  all-important  feature  of  the  design  of  a 
transformer,  and  it  is  often  necessary  to  repeatedly  alter  the 
design  until  a  satisfactory  result  is  reached  as  regards  this 
feature. 

The  mean  length  of  the  magnetic  path  may  be  readily  calcu- 
lated or  scaled  oif  from  a  drawing  such  as  that  in  Fig.  36 
(p.  58),  showing  the  dimensions  of  the  core.  In  our  example 
the  mean  length  amounts  to 

2  X  (51  +  8,5)  +  4X7  =  147 -1 

The  core  has  a  section  of  63,6  sq  cm,  and  consequently  the 
volume  of  the  steel  is 

63,6  X  147  =  9350  cu  cm. 

One  cu  cm  of  steel  weighs  approximately  7,8  grams,  and  thus 
the  total  weight  of  the  core  amounts  to 

0,0078  X  9350  =  73,0  kg. 

We  are  now  in  a  position  to  estimate  the  probable  loss  in  the 
core  of  our  transformer  due  to  hysteresis  and  eddy  losses,  and 
for  this  purpose  we  shall  employ  the  curves  in  Fig.  16  (p.  37), 

1  In  this  estimate,  no  allowance  is  made  for  the  shortening  of  the  magnetic 
path  by  the  curvature  of  the  lines  at  the  corners.  Thus  a  small  factor  of  safety 
is  provided,  and  there  is  the  further  convenience  that  the  volume  of  the  core  is 
equal  to  the  length  of  the  magnetic  path  (as  thus  determined),  multiplied  by 
the  net  cross-section. 


60     THE   DESIGN   OF   STATIC   TRANSFORMERS 

which,  as  already  explained,   represent  the  total  specific  core 
loss  values  for  various  densities  and  periodicities. 

In  our  transformer,  the  periodicity  is  50  cycles  per  second 
and  the  density  is  11,5  kilolines  per  sq  cm.  Consequently  the 
specific  core  loss  will  be  2,6  watts  per  kilogram.  The  total 
core  loss  will  thus  he 

2,6  X  78,0  =  190  watts, 

or  0,95  of  1  per  cent,  of  the  rated  output. 

Before  we  can  judge  intelligently  whether  this  is  a  satisfactory 
value  for  the  core  loss,  we  must  discuss  a  quantity  to  which  the 
term  "  annual "  (or  "  energy  ")  efficiency  may  he  applied.  If,  as 
will  usually  be  the  case  for  smalttransformers  supplying  lighting 
loads,  the  transformer  is  always  in  circuit,  i.e.,  24  hours  per  day, 
,or  8750  hours  per  year,  the  core  loss  will  amount  to 

8750  X  190 

1nnn =  1660  kw  hr  per  annum. 

1UUU 

The  average  lighting  transformer  is  only  loaded  for  a  very 
small  percentage  of  the  whole  yeaiv  the  precise  percentage 
depending  upon  the  load  factor.  Let  us  assume  that  the  trans- 
former will  be  unloaded  for  80  per  cent,  of  the  whole  year,  and 
that  it  will  operate  at  its  rated  load  for  the  remaining  20  per 
cent,  of  that  time.  In  other  words,  let  us  assume  the  load 
factor  to  be  20  per  cent.  Of  course  in  reality  these  periods  of 
load  and  no  load  are  the  two  extreme  conditions,  and  the  trans- 
former will,  as  the  hours  go  b}r,  carry  loads  of  widely  vary- 
ing amounts  ;  but  it  simplifies  the  ;  calculation  and  introduces 
no  unreasonable  inaccuracy  to  carry  out  our  estimates  on  the 
basis  of  these  two  definite  loads,  no  load  and  full  load,  for 
these  two  definite  percentages  of  the  entire  time.  At  rated 
load  we  have,  in  addition  to  the  core  loss,  an  I2  R  loss  of 
(0,018  X  20  000  =)  360  watts  in  the  transformer  windings. 
Thus  the  P  R  loss  amounts  to 

8750  *  °;2°  X  360  =  630  kw  hr  per  annum, 
4-UUU 


COBE   LOSS   AND   ANNUAL   EFFICIENCY         61 
The  output  from  the  transformer  per  annum  amounts  to 

8750  *  °)2Q  X  20  000  =  35  000  kw  hr 
lUuu 

and  the  input  amounts  to  the  sum  of  the  output,  the  core  loss 
and  the  I2  R  losses  per  annum.  Thus  the  input  per  annum 
is  made  up  of 

Core  loss         .V;         ...       1660  kw.  hr. 

Copper  loss     . ..         .:'.          ...          ...         630      „ 

Output 35  000      „ 


Total  input...  ...    37  290      „ 

The    "annual"    efficiency   (or,    preferably,    the    "energy" 
efficiency)  is  consequently  equal  to 

35  000  X  100 

.8X290  ~-  9B'9  Per  Cent' 

Now  although,  as  already  stated  on  p.  53,  in  practice  certain 
advantages  usually  accrue  from  designing  standard  transformers 
for  the  same  regulation,  and  consequently  with  approximately 
the  same  copper  loss,  let  us,  nevertheless,  consider,  in  com- 
parison with  the  transformer  we  have  just  designed  and  which 
we  may  designate  as  Transformer  A,  an  alternative  which  we 
shall  designate  as  Transformer  B.  Whereas  in  Transformer  A 
the  copper  loss  at  rated  load  amounts  to  1*8  per  cent,  of  the 
rated  output  (i.e.,  to  360  watts)  and  the  core  loss  to  0*95  per 
cent,  of  the  rated  output  (i.e., -to  190  watts),  let  us  in  Trans- 
former B  precisely  reverse  these  values  and  proportion  it  for 
a  copper  loss  at  rated  load  of  only  190  watts  and  for  a  core  loss 
of  360  watts.  While  this  leads  to  a  cheaper  design  as  regards 
the  aggregate  cost  for  copper  and  iron,  it  must  be  provided 
with  just  as  large  a  case  as  the  former  design,  since  the  total 
internal  losses  at  rated  load  are  the  same,  and  it  will  conse- 
quently be  necessary  to  provide  the  same  external  radiating 
surface  in  order  to  have  the  same  temperature  rise  when 
operating  at  rated  load. 


62     THE   DESIGN   OF   STATIC   TEANSFOEMEES 


Let  us  now  study  the  "  annual "  efficiency  of  Transformer  B. 

190  X  8750  X  0,2 


The  I2  B,  loss  per  annum  is  equal  to 
320  kw  hr. 

The  core  loss  per  annum  is  equal  to 

kw  hr. 

The  output  per  annum  is  equal  to 


1000 

/360  X  8750 
{        1000 


3150 


/8750  X  0,20  X  20  000  _ 


V 


1000 


35  000  kw  hr. 

Thus  the  input  to  the  transformer  per  annum  is  made  up  of: — 


Core  loss 
Copper  loss    . 
Output  . 


.     3150  kw  hr 
•       330  „    „ 
.35000  „    „ 


Total  input       .  38  480 


" Annual"  (or  "energy")  efficiency  .  91  per  cent. 

We  have  assumed,  however,  that  the  load  factor  on  the  trans- 
former is  20  per  cent.  If  similar  calculations  are  made  for 
different  load  factors  for  each  of  these  two  transformers  we 
obtain  the  results  set  forth  in  Table  6  : — 

TABLE  6.— "ANNUAL"  (OR  "ENERGY")  EFFICIENCY  OF  20-KW 
TRANSFORMER  FOR  VARIOUS  LOAD  FACTORS. 


"  Annual  efficiency"  in  per  cent. 

Load  factor 
(per  cent.). 

Transformer  A.  (Copper 
loss  360  watts,  Core 

Transformer  B.  (Copper 
loss  190  watts,  Core 

loss  190  watts.) 

loss  360  watts.) 

5 

83,0 

73,2 

10 

90,0 

84,0 

15 

92,7 

88,4 

20 

93,9 

91,0 

30 

95,5 

93,6 

40 

96,0 

95,0 

50 

96,5 

95,8 

80 

97,2 

96,5 

100 

97,3 

97,3 

COBE   LOSS  AND   ANNUAL   EFFICIENCY        68 

The  results  obtained  in  Table  6  are  plotted  in  Fig.  87,  and 
it  will  be  seen  that  for  a  load  factor  of  20  per  cent,  the 
difference  in  annual  efficiency  of  Transformers  A  and  B  is 
some  3  per  cent.,  whereas  when  the  load  factor  is  increased 
to  40  per  cent,  the  difference  is  only  some  1  per  cent.  It  is 


100 


3Z  48  64 

Load  factor  /n. 


30 


-  /  Copper  Loss  36O  Hfatts 

Our  re    A  *   Transformer  /7  \C6re,          ••      /3^? 


1  Cooper  loss   /0O  Watts 
Core        » 


FIG.  37.—  Annual  efficiencies  of  20-kw  transformers  at  various  load  factors. 

very  rare,  however,  that  a  lighting   load  factor   as   high  as 
40  per  cent,  or  even  30  per  cent,  is  attained  in  practice. 

Let  us  continue  the  comparison  between  the  two  trans- 
formers from  a  basis  of  the  cost  of  these  different  losses.  On 
the  assumption  that  the  electricity  supply  company's  total 
cost  amounts  to  2d.  per  kw  hr  delivered  to  the  primary  of  the 


64     THE   DESIGN   OF   STATIC   TRANSFORMERS 

transformers,  and  that  the  load  factor  on  the  transformer  is 
20  per  cent.,  the  cost  per  annum  with  Transformer  A  amounts 
to  only  £311,  as  against  £321  for  Transformer  B.  This 
assumption  for  the  cost  per  kw  hr  is  not  quite  correct,  because 
the  copper  loss  will  necessarily  correspond  to  a  greater  outlay 
per  kw  hr  than  the  core  loss,  the  latter  being  equivalent  to  a 
load  of  100  per  cent,  load  factor  and  the  former  being  equivalent 
to  a  variable  load,  and  therefore,  as  such,  the  cost  per  kw  hr 
will  also  be  variable.  For  a  load  factor  of  20  per  cent,  the 
cost  per  kw  hr  of  copper  loss  will  amount  to  some  1,5  to  2 
times  the  cost  per  kw  hr  of  core  loss.  For  our  present  purpose, 
however,  let  us  assume  the  same  price  per  kw  hr  for  both  the 
copper  and  the  core  losses.  In  fact,  the  circumstance  that  the 
core  loss  at  no  load  is  associated  with  a  very  low  power  factor, 
may  largely  or  fully  offset  the  advantage  that  it  represents  a  load 
of  100  per  cent,  load  factor.  Suppose  that  with  both  trans- 
formers the  customer  pays  3d.  per  kw  hr  delivered  from  the 
secondary  ;  then  in  both  cases  he  pays 

35  OOP  X  3  _ 
240 

If  Transformer  A  is  employed,  the  electricity  supply  company's 
annual  gross  profit  is  £126,  as  against  only  £116  when  Trans- 
former B  is  used.  The  "  annual "  efficiency  may,  as  already 
stated,  appropriately  be  termed  the  "energy"  efficiency,  as  it 
is  the  ratio  of  the  energy  output  to  the  energy  input.  This 
distinguishes  it  from  the  conception  to  which  the  term  efficiency 
is  usually  applied.  This  usual  conception  may  appropriately 
be  termed  the  "  power  "  efficiency. 

Let  us  at  this  point  bring  together,  as  in  Table  7 /the  data 
of  losses  and  efficiency  of  these  two  designs,  which  we  have 
designated  A  and  B. 


COEE   LOSS   AND   ANNUAL  EFFICIENCY        65 


TABLE  7.— DATA  OF  LOSSES  AND  EFFICIENCIES  OF  Two  20-KvA 
TBANSFOBMEES. 


Designation. 

A. 

13. 

Copper  loss  at  rated  load  of  20  kw  . 
Core  loss  at  all  loads        .... 
Output  at  rated  load       .... 

Input  at  rated  load          .         .         ;.   ,    .  . 
Power  efficiency  at  rated  load 
,,                .,         half  load  . 
,  ,               ,  ,         one-tenth  load 

360  watts 
190      „ 
20  000      ,, 

190  watts 
360      ,, 
20  000      ,, 

20  550      ,, 

97,5% 
97,5% 
83,6% 

20550      ,, 

97,5% 
95,5% 
73,5% 

Loss    on    open    secondary    circuit    per 
annum  (8750  hr)  
Copper  loss  per  annum  (rated  load  for 
20%  of  time  and  no  load  for  80%  of 
time)    
Output  per  annum  (rated  load  for  20% 
of  time  and  no  load  for  80%  of  time)  . 

Input  per  annum    
"Annual"     efficiency    (or    "Energy" 
efficiency)             ..... 
Supply  company's  total  costs  per  kw  hr 
delivered  to  primary  of  transformer    . 
Annual  cost  to  supply  company 
Charge  to  customer  per  kw  hr  delivered 
from  secondary  circuit 
Annual  revenue  from  customer 
Gross  profit  to  supply  company 

1660  kw  hr 

630     ,, 
35000     ,, 

3150  kw  hr 

330      ,, 
35000     ,, 

37290     „ 
93,9% 

2d.  per  kw  hr 
£311 

3d.  per  kw  hr 
£437 
£126 

38480      ,, 

91,0% 

2d.  per  kw  hr 
£321 

3d.  per  kw  hr 
£437 
£116 

In  a  similar  manner  we  may  calculate  the  profits  accruing  to 
the  supply  company  at  other  load  factors  as  set  forth  in  Table  8. 

TABLE  8.— PEOFITS  OBTAINED   BY    ELECTEICITY   SUPPLY  COMPANY  AT 
VAEIOUS  LOAD  FACTOES,  AND  FOE  TEANSFOEMEES  A  AND  B. 


Transformer  A. 

Transformer  B. 

(Copper  loss  =  360  watts 

(Copper  loss  —  190  watts 

Load  Factor, 

Core  loss  =  190  watts.) 

Core  loss  =  360  watts.) 

in  per  cent. 

Profit  in  £  Ster- 
ling per  Annum. 

Profit  as  per  cent, 
of  Cost  of  Power 
supplied  to 
Transformer. 

Profit  in  £  Ster- 
ling per  Annum. 

Profit  as  per  cent, 
of  Cost  of  Power 
supplied  to 
Transformer. 

5 

21 

22,5 

9 

9,0 

10 

57 

35,2 

33 

20,1 

20 

126 

40,5 

116 

36,1 

40 

2H8 

44,1 

260 

42,3 

50 

335 

44,4 

326 

42,3 

80 

550 

45,9 

540 

44,7 

100 

690 

46,0 

690 

46,0 

66      THE   DESIGN   OF  STATIC   TEANSFOEMEES 


The  results  in  Table  8  are  plotted  in  Fig.  38,  in  which  it 
will  be  seen  that  while  Transformer  A  has  a  decided  com- 
mercial advantage  over  Transformer  B  at  low  load  factors, 
this  advantage  decreases  with  higher  load  factors. 

In  view  of  the  considerable  saving  thus  effected,  the  reader 


/&  32.  *4Q  64-  QO  &6 

Load  factor /n  fercenb 


^  . 

/ransf 


ormer 


Co 


onner 
Ztv 


toss  360  /YMs 


^  /  Coffer  Loss  /SO 


FIG.  38.  —  Profit  to  electricity  supply  company  in  per  cent,  of  cost  of 
power  supplied  to  20-kw  transformers  at  various  load  factors. 

will  be  inclined  to  inquire  whether  the  20-kw  transformer 
should  not  be  designed  for  a  still  lower  core  loss  than  190  watts. 
Any  considerable  reduction  in  the  core  loss  below  the  value 
of  190  watts  already  obtained  in  Transformer  A  would  only  be 
obtained  by  a  design  with  a  regulation  distinctly  worse  than 
2  per  cent.  This  is  not  desirable.  The  reader  may  be 


COEE   LOSS   AND   ANNUAL   EFFICIENCY         67 

interested  to  try,  with  the  limitation  of  2  per  cent,  regulation 
(1,8  per  cent.  I R  drop),  to  work  out  a  design  with  a  lower  core 
loss.  It  may  be  said,  however,  that  (even  with  no  limitation  as 
regards  outlay  for  material)  no  very  radical  improvement  can 
be  obtained  with  the  grades  of  material  at  present  available. 

In  a  general  way  the  reasons  for  this  may  be  made  clear. 
The  current  at  no  load,  a  further  discussion  of  which  will  be 
given  later,  will  be  greater  than  is  desirable  if  we  push  the 
saturation  up  much  beyond  11,5  kilolines.  Hence  the  quantity 
of  iron  cannot  be  decreased  by  employing  higher  saturation. 
With  the  same  magnetic  circuit,  but  with  lower  saturation, 
the  watts  per  kilogram  decrease,  but  as  the  total  magnetic 
flux  is  decreased  the  turns  must  be  proportionately  increased, 
and  in  order  that  the  I  H  drop  shall  not  be  decreased  a  larger 
section  of  conductor  is  necessary.  The  original  winding  space 
(or  "window")  thus  becomes  altogether  inadequate,  and  by 
the  time  it  is  increased  to  sufficient  size  to  contain  the  wind- 
ings, the  mean  length  of  the  magnetic  circuit  will  have  become 
so  increased  as  to  increase  the  weight  of  iron  to  nearly  or 
quite  as  great  an  extent  as  the  watts  per  kilogram  in  the  iron  have 
been  decreased  by  lowering  the  saturation.  Thus  no  consider- 
able decrease  in  the  core  loss  can  be  effected.  Slight  modification 
may,  it  is  true,  be  effected  by  a  wider  and  shorter  winding 
space,  as  also  by  alteration  in  the  cross-section  of  the  magnetic 
circuit,  and  it  is  in  obtaining  the  most  suitable  proportions  in 
these  various  respects  that  the  designer's  skill  m-ay  be  dis- 
played. It  requires,  however,  not  so  much  skill,  as  patient 
perseverance  and  trained  instinct.  It  is  a  very  tedious  process 
to  work  out  the  large  number  of  alternative  designs  required 
to  ensure  obtaining  the  best  results,  and  it  has  been  largely 
the  temptation  to  avoid  this  tedious  work  which  has  led  to 
the  concocting  of  formulae  devised  with  the  purpose  of  arriving 
at  the  truly  economical  design  by  simple  substitution.  The 
assumptions  entering  into  these  formulae,  however,  render 
them  of  little  or  no  use  to  the  practical  designer. 

F  2 


CHAPTER    IV 

NO-LOAD    CURRENT,    POWER   FACTOR   AND    EFFICIENCY 

WHEN  the  secondary  circuit  of  a  transformer  is  open  (i.e., 
when  the  transformer  is  unloaded)  there  is  a  certain  current 
flowing  through  the  primary  circuit  from  the  source  of  supply, 
and  this  is  commonly  termed  the  "no-load"  current.  The 
"  no-load  "  current  is  the  resultant  of  two  components,  namely, 
the  current  necessary  to  magnetise  the  core  to  the  required 
density  and  the  core  loss  current.  The  calculation  of  the 
magnetising  current  will  be  taken  up  first.  In  the  case  of 
the  20-kw  transformer  the  procedure  is  as  follows  : — 

Magnetic  density  in  core  =  11,5  kilolines  per  sq  cm. 

Corresponding  specific  magnetomotive  force  in  ampere 
turns  per  centimeter  of  length  of  magnetic  circuit  (from 
Fig.  10,  on  p.  34)  =  6,0  ampere  turns  per  cm. 

Mean  length  of  magnetic  circuit  (from  Fig.  36,  on  p.  58)  .= 
147  cm. 

Total  magnetomotive  force  required  to  send  the  flux  round 
the  magnetic  circuit  =  (6,0  X  147  =)  890  ats. 

The  primary  winding  comprises  3100  turns.  Consequently, 
in  order  to  provide  the  required  magnetomotive  force  of 
890  ats,  the  crest  value 'of  the  magnetising  component  of  the 
no-load  current  must  be  equal  to 

=  0,286  ampere.  || 

The  virtual  value  of  the  magnetising  component  works  out  at 
^~  =  0,202  ampere. 

Obviously  the  above  result  involves  the  assumption  that  the 
mngnetising  component  is  sinusoidal  in  form. 


NO-LOAD   CUEEENT,   POWEE   FACTOE,   ETC.      69 


Let  us  now  consider  the  other  component  of  the  no-load 
current,  namely,  the  core-loss  component.  This  is  obtained 
by  dividing  the  core  loss,  in  watts,  by  the  primary  pressure. 
Thus  the  core-loss  component  in  our  20-kw  design  is  found 

to  be 

1QO 

=  0,038  ampere. 


Core  Loss  Component 
0,033  Amperes. 

FIG.  39. — No-load  current  diagram. 


These  two  components, 
the  magnetising  compo- 
nent and  the  core-loss 
component,  are  in  quad- 
rature with  one  another 
and  may  be  represented 
as  shown  in  Fig.  39,  in 
which  O  A  is  the  mag- 
netising component  (0,203 
ampere),  0  B  the  core- 
loss  component  (0,038 
ampere),  and  0  C  is  the 
resultant  of  these  two 
components,  and  is  termed 
the  "  no-load  "  current.  In  this  case  it  amounts  to 

\/0,2032  X  0,038'2  =  0/205  ampere. 

The  power  factor,  G,  is  obviously  the  ratio  of  the  core-loss 
component  to  the  resultant  or  "  no-load  "  current,  and  is,  at 
no  load,  equal  to 

0,038 

0,205 

It  may  be  of  interest  to  estimate  the  inductance1  of  the 
primary  winding  when  there  is  no  load  on  the  secondary,  i.e., 
when  the  primary  winding  is  carrying  0,205  ampere.  The 

1  In  a  chapter  entitled  "  Inductance "  in  my  little  treatise  "  Electricity  " 
(Constable,  London,  1910),  I  endeavour  to  explain  the  subjects  of  reactance  and 
impedance  in  a  way  which  I  conceive  should  be  helpful  to  the  practical  engineer 
who  is  disinclined  towards  mathematical  methods. 


70      THE    DESIGN   OE    STATIC    TEANSFOKMERS 

reactance  S  in  ohms  is  the  quotient  of  the  terminal  pressure 
and  the  magnetising  component,  and  hence  is  equal  to 

=  24,700  ohms.  .    •, 

The  reactance  S  is,  however,  also  equal  to  2  IT  oo  l}  where  I  is 
the  inductance  in  henrys.     Therefore 
,  24  700 

=  2^<V^O  =~-  7 

The  inductance  might  also  have  been  estimated  in  the  follow- 
ing manner.  Since  ,  the  total  ^dux  passing  through  the  iron 
core  is  equal  to  0,73  megalines,  and  since  the  magnetising 
component  of  the  no-load  current  is  equal  to  0,203  amp 
(or  0,203  X  A/2  =  0,286  crest  ampere),  the  flux  per  ampere 
becomes  equal  to 

0,73 

—  =  2,55  megalines. 


0,286 

There  are  3100  primary  turns,  and  therefore  the  inductance 
may  be  found  as  follows  : — 

3100  X  2  550  000 
I  =  -          ~TO« —         -  =  79  henrys. 

We  have  seen  on  the  previous  page  that  for  the  power 
factor,  G,  of  our  20-kw  transformer,  we  have,  at  no  load, 
the  value 

G  =  0,185. 

The  power  factor  increases  rapidly  as  the  load  on  the  trans- 
former increases.  We.  have  seen  that  at  no  load  the  wattless 
component  of  the  current  flowing  into  the  transformer  (i.e.,  the 
magnetising  component)  is  0,203  ampere,  and  that  the  energy 
component  (i.e.,  the  core-loss  component)  is  0,038  ampere.  The 
full  load  secondary  current  is  100  amperes.  When  the  secondary 
current  is  10  amperes  there  must  be  an  equivalent  energy  com- 
ponent flowing  into  the  primary  windings  to  provide  it. 
Since  the  ratio  of  transformation  is  (5000  :  200  =  )  25  :  1, 
this  energy  component  flowing  into  the  primary  will  be 


NO-LOAD   CURRENT,   POWER  FACTOR,   ETC.      71 

(  25  =  )  °>40  ampere.    This  is  in  addition  to  the  core-loss  com- 

ponent of  0,038  ampere.  Consequently,  when  the  secondary 
load  is  10  amperes  at  unity  power  factor,  the  primary  current 
is  made  up  of  two  components,  the  magnetising  component 
of  0,203  amp.  and  an  energy  component  of  (0,40  +  0,038  =) 
0,438  ampere.  The  resultant  current  flowing  into  the  primary 
is  equal  to 

A/0,2032  +  0,438a  =  0,484  ampere. 

Consequently,  for  the  power  factor  at  one-tenth  load  we 
have 


Similarly,  when  the  energy  component  of  the  primary 
current  has  increased  to  1,00  ampere,  the  resultant  current  is 
equal  to 

VO,2032  +  1,002  =  1,02  ampere 
and  the  power  factor  becomes 


The  results  of  these  few  examples  show  clearly  that  the 
power  factor  at  first  increases  very  rapidly  for  a  small  increase 
in  the  energy  component,  and  that  at  comparatively  small 
loads  the  power  factor  usually  reaches  a  high  value.  By 
similar  calculations,  power  factors  for  other  values  of  the 
energy  component  may  be  obtained,  and  from  them  the  power 
factor  curve  of  Fig.  40  may  be  plotted.  When  the  secondary 
load,  instead  of  being  non-inductive,  has  a  power  factor  of  less 
than  unity,  the  primary  power  factor  will,  for  all  usual  designs, 
be  substantially  the  same  at  any  load  as  the  secondary  power 
factor. 

The  efnciencj"  at  various  loads  may  be  obtained  as  shown 
in  Table  9.  In  the  first  two  columns  the  load  on  the  trans- 
former is  given.  The  third  column  contains  the  core  loss, 


72      THE   DESIGN   OF   STATIC   TRANSFORMERS 


which,  of  course,  is  substantially  independent  of  the  load.  The 
third  column  contains  the  copper  loss,  the  fourth  the  total 
input  to  the  transformer,  this  being  equal  to  the  sum  of  the 

/00\ 


Zoad  on   Ts&nsfor/ner 

FIG.  40. — Curve  showing  variation  of  power  factor  with  the  load  for  a 
20-kw  transformer. 

three  previous   columns.     The   "power"   efficiency,  i.e.,  the 
ratio  of  column  2  to  column  5  is  given  in  column  6. 

TABLE  9. — EFFICIENCY  DATA  OF  20-KW  TRANSFORMER. 


Load  on  Transformer. 

Core  loss 
in  kw. 

Copper  loss 
in  kw. 

Input  to 
Transformer 
in  kw. 

Power 
efficiency 
in  per  cent. 

Per  cent. 

Kw 

Full  load. 

10 

2 

0,19 

0,0036 

2,194 

91,20 

25 

5 

0,19 

0,0225 

.    5,213 

95,95 

50 

10 

0,19 

0,090 

10,28 

97,35 

75 

15 

0,19 

0,202 

15,39 

97,50 

100 

20 

0,19 

0,360 

20,55 

97,35 

125 

25 

0,19 

0,563 

25,76 

97,10 

These  values  of  the  efficiency  are  plotted  in  Fig.  41,  where 


NO-LOAD   CURRENT,   POWER  FACTOR,   ETC.      73 


are  also  given  the  losses  as  a  percentage  of  the  load,  and  the 
regulation  for  various  non-inductive  loads. 


74     THE   DESIGN   OF    STATIC   TRANSFORMERS 


In  contrast  to  the  above  transformer  there  are  given  in 
Table  10  the  efficiencies  of  a  20-kw  transformer  having  a  core 
loss  of  360  watts  and  a  copper  loss  at  rated  load  of  190  watts. 
The  values  in  Table  10  are  plotted  in  Fig.  42. 

TABLE  10. — EFFICIENCY  DATA  OF  20-KW  TRANSFORMER. 


Load  on  Transformer. 

Core  loss 
in  k\v. 

Copper  loss 
in  kw. 

Input  to 
Transformer 
in  k\v. 

"  Power  " 
efficiency 
in  per  cent. 

Per  cent. 
Full  load. 

Kw. 

10 

2 

0,36 

^0,002 

2,36 

84,68 

25 
50 
75 

5 
10 
15 

0,36 
0,36 
0,36 

0,012 
0,048 
0,107 

5,37 
10,41 
15,47 

93,12 
96,10 
97,00 

100 
125 

20 
25 

0,36 
0,36 

0,190 
0,297 

20,55 
25,66 

97,40 
97,46 

With  the  employment  of  modern  high-grade  transformer 
laminations  the  core  can  be  worked  at  much  higher  flux 
densities  for  the  same  core  loss  per  kilogram  than  with  the  best 
grades  available  three  or  four  }*ears  ago.  But  when  the  core  is 
worked  at  high  densities,  the  no-load  current  is  considerably 
increased.  This  is  illustrated  in  Fig.  43,  in  which  the  upper 
curve  represents  the  percentage  no-load  current  for  a  line  of 
transformers  in  which  modern  high-grade  laminations  worked 
at  high  densities  are  employed,  and  the  lower  curve  represents 
this  factor  for  a  line  of  transformers  built  some  few  years  ago 
and  employing  the  best  material  then  available.  The  core 
loss  per  kilogram  is  about  the  same  in  both  cases  for  designs 
for  a  given  rated  output,  and  the  greater  percentage  no-load 
current  is  due  chiefly  to  the  higher  densities  employed  in 
the  modern  designs.  In  fact,  the  densities  employed  run 
up  considerably  higher  than  is  desirable  in  the  case  of  the 
smaller  rated  outputs  for  the  modern  designs,  since  the  low 
power  factors  at  light  loads  would  constitute  a  distinctly 
undesirable  feature  from  the  supply  company's  standpoint. 


NO-LOAD   CUEKENT,   POWER  FACTOR,   ETC.       75 

In  Fig.  44  have  been  plotted  values  of  the  core  loss  as  a 
function  of  the  rated  output  for  several  lines  of  designs.  These 
values  have  been  taken  from  the  published  data  of  several  large 
manufacturing  firms,  and  they  are  for  transformers  of  the 
various  periodicities  indicated  in  the  figure.  Most  of  the 
designs  now  (1910)  on  the  market  are  proportioned  for  still 
lower  core  losses,  since  alloyed  steel  is  now  almost  universally 
employed.  It  will  be  observed  that  for  the  same  manufacturing 


FIG.  43.— Curves  showing  the  relation  between  the  no-load  current  and  the 
rated  output  for  transformers  having  (A)  high  grade  and  (B)  ordinary 
grade  laminations. 

firm  the  higher  the  periodicity  the  lower  is  the  core  loss.  This 
is  because  a  standard  transformer  designed  for  a  periodicity  of, 
say,  50  cycles  per  second  is  often  also  supplied  for  use  on 
circuits  of  periodicities  from  50  cycles  upwards.  If  the  50- 
cycle  standard  transformer  is  placed  on  a  100-cycle  circuit, 
the  flux  density  is  halved.  Since  the  hysteresis  loss  constitutes 
a  larger  percentage  of  the  total  core  loss  than  does  the  eddy 
current  loss,  a  considerable  reduction  in  the  core  loss  results. 
As  a  rule,  however,  a  25-cycle  circuit  requires  a  new 


76      THE  DESIGN   OF   STATIC  TRANSFORMERS 

design,  for  if  the   standard   50-c3Tcle  transformer  is  used  for 
this  periodicity,  the  flux  density  becomes  doubled,  and  if  the 


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density  is  already  high  when  operating  from  a  50-cycle  circuit, 
the  core  would,  at  25-cycles,  then  become  too  highly 
saturated,  hence  a  large  magnetising  current  would  be  required, 


NO-LOAD   CUERENT,   POWER  FACTOR,  ETC.       77 


which  would  result  in   a  low  power  factor.     If,   on  the  other 
hand,   the   density    when    working    on   a   50-cycle    circuit  is 


78      THE    DESIGN   OF    STATIC   TRANSFORMERS 

exceptionally  low,  then  it  might  be  admissible  to  use  the  same 
design  on  a  25-cycle  circuit.  These  proportions  are  not, 
however,  such  as  yield  the  best  results  at  50-cycles. 

The  influence  of  the  periodicity  upon  the  core  loss  and 
upon  the  no-load  current  of  our  20-kw  transformer  is  shown 
in  Fig.  45.  By  increasing  the  periodicity  from  50  cycles  to 
100  cycles  the  core  loss  has  been  decreased  from  190  watts  to 
125  watts,  but  by  decreasing  the  periodicity  to  40  cycles  the 
core  loss  has  been  increased  to  240  watts.  The  variations  in 
the  no-load  current,  due  to  various  periodicities,  is  still  more 
striking.  Fig.  46  shows  the  influence  of  supplying  different 
pressures  to  the  primary  terminals^  upon  the  core  loss  and  the 
no-load  current. 

In  Fig.  47  are  given  curves  showing  the  relation  between 
the  regulation  and  the  output,  corresponding  to  some  of  the 
curves  shown  in  Fig.  44.  From  these  curves  it  is  seen  that  in 
three  cases  the  regulation  is  closer  the  greater  the  rated  out- 
put, and  in  another  case  it  is  the  same  for  all  rated  outputs. 
Close  regulation  may  be  obtained  either  by  working  the  copper 
at  a  low  current  density  in  which  case  a  fairly  large  number  of 
turns  may  be  employed  and  a  small  flux,  or  it  may  be  obtained 
by  employing  a  considerably  higher  current  density,  a  small 
number  of  turns,  and  a  large  flux.  The  latter  plan  generally 
results  in  a  greater  core  loss  than  the  former  plan. 

Comparing  our  20-kw  design,  as  regards  core  loss  and 
regulation,  with  the  data  just  given  for  various  lines  of  trans- 
formers, we  find  that  the  design  is  fairly  in  accord  with  good 
practice  as  relates  to  these  quantities.  Of  course,  the 
designer's  object  is  to  obtain  a  good  result  at  a  minimum  total 
works  cost,  and  designs  should  also  be  compared  from  this 
point  of  view.  Broadly,  however,  it  may  be  said  that  what 
might  appear  an  extravagant  outlay  when  the  cost  of  the 
copper  and  core  is  alone  considered,  often  constitutes  but  a 
very  inappreciable  increase  in  the  cost  by  the  time  the  cost  of 
the  oil,  the  insulation  materials,  the  case,  the  bushings  and  the 


NO-LOAD   CURRENT,   POWER  FACTOR,   ETC.     79 

leads,  as  also  of  the  labour  and  of  the  establishment  charges, 
are  all  taken  into  account.  In  large  concerns  it  is  a  very 
common  occurrence  (attributable  to  poor  administration)  that 


the  establishment  charges  mount  up  to  a  very  formidable  per- 
centage of  the  total  works  cost,  whereas  in  a  very  small  concern 
these  charges  are  often  kept  down  to  a  small  percentage  by  the 
exercise  of  strenuous  oversight.  While  it  might  at  first  glance 


80     THE   DESIGN   OF   STATIC   TKANSFOKMERS 

appear  that  a  consequence  of  this  state  of  affairs  would  be  that 
the  smaller  concern  could  meet  the  price  even  with  a  more 
liberal  outlay  for  material,  further  reflection  will  show  that 
on  account  of  the  smaller  percentage  of  the  total  cost  repre- 
sented by  establishment  charges,  a  given  percentage  saving 


"     £$ 


FIG.  48.  —  Curves  showing  ratio  of  labour  cost  to  cost  of  active  material  for 
natural  air-cooled  and  oil-cooled  transformers. 

effected  in  the  outlay  for  materials  makes  a  greater  percentage 
reduction  in  the  total  works  cost  than  a  corresponding 
percentage  saving  in  materials  in  the  case  of  a  large  firm  with 
abnormal  establishment  charges. 

In  view  of  this  latter  consideration  and  of  various  disadvan- 
tages under  which  the   smaller  firm  conducts  its  business,  it 


AX) 


NO-LOAD   CUEKENT,   POWEK  FACTOR,   ETC.    81 

will  appear  fairly  conclusive  that  the  large  firm  can  go  further 
in  the  direction  of  a  liberal  outlay  for  material,  so  long  as  a 
reasonable  improvement  in  quality  is  thereby  attainable,  than 
can  a  small  firm.  Of  course,  in  many  individual  cases  these 
general  characteristics  of  small  and  large  firms  are  completely 
reversed,  and  in  such  cases  the  reverse  conclusions  would  hold. 
Some  curves  showing  the  approximate  ratio  of  labour  cost  to 
active  material  cost,  i.e.,  copper  and  iron  (and  oil  for  oil-cooled 
transformers),  are  shown  in  Fig.  48  for  both  natural  air-cooled 
and  oil-cooled  transformers  of  various  capacities.  The  cost  of 
the  insulating  materials  is  not  included  in  the  results  from 
which  these  curves  are  plotted.  But  it  is  important  to 
consider  the  cost  of  the  material  in  a  transformer  as  made 
up  of:— 

I.  Core. 
II.  Copper. 

III.  Insulating  materials. 

IV.  Oil. 
V.  Case. 

VI.  Accessories  (such  as  bushings,  etc.). 


S.T.  G 


CHAPTER    V 

THE    DESIGN    OF    THE    WINDINGS   AND    INSULATION 

LET  us  now  proceed  to  design  the  windings  and  insulation 
more  in  detail.  An  outline  drawing  showing  the  location  of  the 
windings  for  this  design  is  given  in  Fig.  49.  The  secondary 


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FlG.  49. — Outline  drawing  showing  the  arrangement  of  the  windings 
of  the  20-kw  5000/200-volt  transformer. 


DESIGN   OF   WINDINGS  AND   INSULATION       83 

coils  are  wound  the  full  length  of  each  of  the  long  vertical 
cores.  We  have  already  ascertained  that  we  shall  require  124 
secondary  turns  and  3100  primary  turns.  Thus  each  secondary 
coil  must  contain  62  turns.  The  secondary  conductor  is  com- 


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FlG.  50. — Sectional  drawing  showing  details  of  primary  and  secondary  windings 
for  a  20-kw  5000/200-volt  single-phase  transformer. 

posed  of  four  flat   strips,  each,  when  bare,  measuring  2,0  mm 
X  6,8  mm. 
The  total  section  of  the  secondary  conductor  thus  amounts  to 

4  X  2,0  X  6,8  =  54,5  sq  mm, 

which  is  the  value  already  estimated  (on  p.  54)  to  be  required. 
These  four  component  strips  are  laid  one  above  the  other,  as 
indicated  again  to  a  large  scale  in  Figs.  50  and  51,  and  are 

G2 


84      THE   DESIGN   OF   STATIC   TRANSFORMERS 


\   Turns 

Jj  '^Component  Coil 
6  ^.BareDia 
*>^.lnsul.  „ 


51  —Drawing  showing  details  of  primary  and  secondary  windings  for  a 
20-kw  5000/200-volt  single-phase  transformer. 


DESIGN   OF   WINDINGS   AND   INSULATION      85 

taped  together  to  constitute  a  single  conductor,  measuring  over 
the  insulation  8,7  X  7,5  mm.  The  62  turns  are  wound  in  a 
single  layer  occupying  (62  X  0,75  =)  46,5  cm  of  the  51  cm 
total  length  of  winding  space. 

The  secondary  coils  are  in  the  present  case  designed  to  be 
wound  directly  upon  the  cores,  strips  of  sufficient  thickness  of 
suitable  insulating  material  being  interposed  between  the 
laminated  cores  and  the  secondary  coils.  While  ventilating 
spaces  for  oil  circulation  are  in  themselves  advantageous,  the 
internal  winding  space  (i.e.,  the  space  represented  by  the 
winding  "  window  ")  must  often  be  regarded  as  too  valuable 
to  be  devoted  to  this  purpose,  since  the  values  of  the  core  loss 
and  of  the  regulation  are  very  dependent  upon  the  efficient 
utilisation  of  the  winding  window. 

But  on  the  outer  sides,  ventilating  spaces  are  much  more 
justifiable,  and  in  the  present  design  a  clear  space  of  10  mm 
depth  is  provided,  as  indicated  in  Figs.  50  and  51.  The 
secondary  coils  are  held  at  this  distance  from  the  core  by  wooden 
corner  strips,  and  the  laminations  are  left  bare  with  a  view  to 
more  efficient  heat  emission  to  the  circulating  oil.  The  coils 
may,  as  an  alternative,  be  form- wound,  slipped  over  the  cores 
and  wedged  in  place.  The  general  plan  has  already  been 
illustrated  in  Fig.  29  (p.  49).  It  is  an  instance  of  an  arrange- 
ment which  I  have  widely  used.  Various  detail  features  of  the 
arrangement  of  cores  and  windings  are  described  in  my  British 
Patent  No.  26412  of  1897.  The  insulation  between  the 
secondary  and  primary  coils  is  in  this  instance  of  a  thickness 
of  3,5  mm.  Any  of  several  excellent  insulating  materials,  when 
suitably  built  up  to  this  thickness,  will  afford  a  barrier  capable  of 
readily  withstanding  the  application  of  a  test  at  15  000  virtual 
volts  for  five  minutes.  A  curve  to  which  I  usually  work  in  the 
proportioning  of  the  main  insulations  of  oil-immersed  trans- 
formers is  given  in  Fig.  52.  This  curve  may  be  safely  used 
when  suitable  insulations  are  intelligently  employed.  With 
relatively  expensive  materials,  lesser  thicknesses  suffice  under 


86     THE   DESIGN   OF   STATIC   TEANSFOEMEES 

certain  circumstances.  On  the  whole,  the  progress  at 
present  being  made  in  the  development  of  improved  insulating 
materials  and  methods  is  making  it  practicable  to  work  with 


/OOOO 


^8000 


4OOO 


2000 


/n  M/ ///meters 

FIG.  52.— Curve  showing  thickness  of  insulation  between  primary  and  secondary 
windings  of  transformers. 

less  thicknesses  than  the  values  corresponding  to  the  curve  in 
Fig.  52. 

The  primary  winding  is  divided  up  into  eight  coils,  four  on 
each  leg,  as  seen  in  Figs.   49   and  51.     Each  coil  is  wound  in 


DESIGN   OF   WINDINGS  AND   INSULATION      87 

nine  layers  with  the  numbers  of  turns  per  layer  set  forth  in 
Figs.  50  and  51.  Fig.  50  shows  in  considerable  detail  the 
general  arrangement  of  one  primary  coil.  The  5000  primary 
volts  are  thus  divided  up  into 

5552  =  625  volts  per  coil, 
o 

This  625  volts  is  again  divided  into  (-Q-  —  )  70  volts  per 

layer  (as  an  average). 

Between  the  extreme  turns  of  two  adjacent  layers  there  is  thus 
on  the  average  a  pressure  of  140  volts.  Had  a  smaller  number 
of  primary  coils  been  employed,  the  pressure  per  layer  would 
have  been  greater,  and  an  uneconomically  large  amount  of  space 
would  have  had  to  be  devoted  to  insulation  between  the 
layers. 


CHAPTER  VI 

THE  INFLUENCE  OF  THE  FREQUENCY 

IT  has  already  been  seated  on  p.  78  that  transformers 
designed  for  a  given  periodicity  may  he  and  are  often  used  on 
circuits  having  periodicities  ahove  that  for  which  they  have 
been  designed.  For  circuits  having  periodicities  below  the 
designed  figure,  the  large  no-load  current  consequent  upon  the 
very  high  densities  in  the  core,  stands  in  the  way  of  their 
successful  use,  the  power  factor  of  the  circuit  being  seriously 
lowered.  Moreover,  the  core  loss  at  the  lower  periodicity  is 
higher.  The  lower  periodicity  in  itself  would  occasion  a 
decrease  in  the  core  loss,  but  the  higher  flux  density  produces 
an  increase  in  the  core  loss  which  more  than  suffices  to  offset 
the  decrease,  and  the  result  is  a  considerably  increased  core 
loss.  It  is,  therefore,  often  necessary  and  usually  preferable  to 
prepare  separate  designs  for  circuits  of  lower  periodicities.  If 
calculations  according  to  the  method  given  in  the  previous 
chapters  are  carried  through  for  two  other  20-kva  oil-cooled 
single-phase  transformers,  differing  as  regards  rating  from  the 
one  we  have  considered,  only  in  respect  to  their  periodicities, 
which  are  respectively  15  c}Tcles  per  second  and  25  cycles  per 
second,  then  the  specifications  given  in  columns  A  and  B  of 
Table  11  will  be  obtained.  Column  C  of  the  same  table  con- 
tains the  data  of  the  50-cycle  transformer  which  we  have  been 
designing.  It  will  be  seen  that  with  the  lower  periodicities 
the  core  loss  has  increased  considerably  above  that  of  the 
design  for  50  cycles  per  second,  notwithstanding  the  much 
greater  amount  of  material  employed. 


THE   INFLUENCE   OF    THE    FEEQUENCY        89 


TABLE  11.— SPECIFICATION  FOR  15-,  25-  AND  SO-CYCLE,  5000  :  200-voi/r, 
20-KVA  SINGLE-PHASE  TRANSFORMERS. 


A. 

B. 

C. 

Periodicity  (in  cycles  per  sec) 

15 

25 

50 

Bated  output  (in  kilo  volt  amperes) 

20 

20 

20 

Primary  pressure  (in  volts) 

5000 

5000 

5000 

Secondary  pressure  (in  volts)       .-       . 

200 

200 

200 

Periodicity  (in  cycles  per  sec) 

15 

25 

50 

Preliminary  assumed  efficiency  from 

Fig.  7,  p.  25  (in  per  cent) 

96,8 

96,9 

97,1 

Efficiency  as  corrected  from  the  final 

calculations  (in  per  cent.) 

97,1 

97,2 

97,3 

Primary  current  (in  amp)   .         .  .      , 

4,13 

4,13 

4,13 

Secondary  current  (in  amp) 
"  Yolts  per  turn  "  (from  Fig.  8,  p.  27) 

100 
1,50 

100 
1,55 

100 
1,60 

Number  of  primary  turns  . 

3300 

3200 

3100 

Elux  (in  megalines)  [M]     . 

2,28 

1,41 

0,73 

Elux  density  (in  kilolines  per  sq  cm)  . 

14,0 

13,5 

11,0 

Net  cross  -section  of  core  (sq  cm) 

163 

104 

66 

Gross            ,,             ,,             „ 

172 

110 

70 

Dimensions  of  core  (cm) 

12,0x14,5 

9  X  12 

7  X  10 

Width  of  winding  window  (cm)  . 

15,5 

11,8 

8,5 

Total  IE  drop  (per  cent.)    .         .  ...     . 

1,8 

1,8 

1,8 

Primary  I  Li  drop  (per  cent.) 

0,9 

0,9 

0,9 

Secondary  1R  drop  (per  cent.)    . 

0,9 

0,9 

0,9 

Primary  resistance  (ohms)  . 

10,8 

10,8 

10,8 

Secondary  resistance  (ohms)        .      .  . 

0,018 

0,018 

0,018 

Mean  length  of  primary  turn  (cm) 

84 

66 

53 

Number  of  secondary  turns 

132 

128 

124 

Mean  length  of  secondary  turn  (cm)  . 

63 

53 

40 

Cross-  section  of  primary  copper  (sq  cm) 

0.052 

0,039 

0,030 

,,         ,,        secondary     ,,         ,, 

0,92 

0,75 

0,54 

Aggregate   cross-section    of    primary 

turns  (sq  cm)  

172 

125 

93 

Aggregate  cross-  section  of  secondary 

turns  (sq  cm)  ..... 

121 

96 

97 

Aggregate   cross  -section    of    primary 

and  secondary  copper  (sq  cm)  . 

293 

221 

160 

"  Space  factor  "  of  winding  window    . 

0,37 

0,37 

0,37 

Gross  area  of  winding  window  (sq  cm) 

790 

600 

435 

Length  of  winding  window  (cm) 

51 

51 

51 

Total  weight  of  sheet  steel  (kg)  . 
Flux  density  (kilolines  per  sq  cm) 

230 
14,0 

134 
13,5 

76 
11,0 

Core  loss  per  kg  (from  Eig.  16,  p.  37). 

1,0 

1,6 

2,5 

Total  core  loss  (watts) 

230 

214 

190 

CALCULATION  OF  NO-LOAD  CURRENT. 

Mean  length  of  magnetic  circuit  (cm) 

182 

166 

147 

Amp  turns  per  cm  (from  Fig.  10,  p.  34) 

12 

10 

5,3 

Total  amp  turns  required    . 

2200 

1660 

780 

Primary  turns 

3300 

3200 

3100 

90     THE  DESIGN  OF   STATIC  TRANSFORMERS 

TABLE  11 — continued. 


A. 

B. 

C. 

CALCULATION  OF  NO-LOAD  CURRENT 

—  continued. 

Crest  value  of  the  magnetising  com- 

ponent of  the  no-load  current  (amp) 

0,67 

0,52 

0,25 

Virtual  value  of  the  magnetising  com- 

ponent of  the  no-load  current  (amp) 

0,47 

0,37 

0,178 

Core  loss  (watts)          .... 

230 

214 

190 

Core   loss  component  of  the  no-load 

current     .         .         .         . 

0,046 

0,013 

0,038 

No-load  current  (amp)         .         . 

0,472 

0,373 

0,182 

Power  factor  at  no  load       .  _}    . 

0,098 

0,115 

0,22 

No-load  current  in  per  cent,  of  cur- 

rent at  full  load       .         .         . 

12 

9 

4,4 

WINDINGS  —  Primary. 

Number  of  primary  component  coils  . 

8 

8 

8 

»             »     per  leg 

4 

4 

4 

Number  of  turns  per  primary  com- 

ponent coil      ..... 

413 

400 

388 

Bare  diameter  of  primary  wire  (mm)  . 

2,57 

2,24 

1,96 

Insulated  diameter   of    primary  wire 

(mm)         ... 

2,75 

2,40 

2,11 

Number  of  turns  per  innermost  layer 

38 

42 

48 

Number  of  layers  of  turns  . 

14 

12 

9 

Dimensions    of    primary    component 

coil  (mm)         ..... 

11  X4,5 

11  X3,4 

11  X  2,4 

Secondary. 

Number  of  secondary  component  coils 

2 

2 

2 

„             M             »             »     per  leg 

1 

1 

1 

Number   of  turns  per  secondary  com- 

ponent coil       

66 

64 

62 

Number  of  strips  in  parallel,  consti- 

tuting one  turn       .... 

5 

4 

4 

Dimensions  of  each  component  strip 

(mm)        

6,6  X  2,8 

6,6  X  2,8 

6,8  x  2,0 

Insulated     dimensions     of    complete 

turn  (mm)        .         ... 

7,3  X  14,7 

7,3  X  11,9 

7,5  x  8,7 

Number  of  layers         .... 

1 

1 

1 

Number  of  turns  per  layer  . 

66 

64 

62 

Dimensions  of  secondary  component 

coil  (cm)  

49  X  1,5 

49  X  1,2 

49  X  10,9 

WEIGHTS. 

Weight  of  primary  copper  (kg)  . 
Weight  of  secondary  copper  (kg) 
Total  weight  of  copper  (kg) 

128 
68 
196 

73 

45 
118 

44 
24 

H8 

Total  weight  of  core  (kg)    . 

230 

134 

76 

Total  net  weight  of  active  material  (kg) 

426 

252 

144 

THE  INFLUENCE   OF   THE  FREQUENCY        91 


TABLE  11 — continued. 


A. 

B. 

c. 

LOSSES. 

Primary  /2  R  loss  at  rated  load  (watts) 

185 

185 

185 

Secondary  I'2  R  loss  at  rated  load(  watts) 

180 

180 

180 

Total  /'2  R  loss  at  rated  load  (watts)     . 

'365 

365 

365 

Core  loss  at  rated  load  (watts)     . 

230 

214 

190 

Total  of  all  losses  (watts)     . 

595 

570 

550 

Output  (watts)    

20000 

20000 

20000 

Input  (watts)       ..... 

20590 

20570 

20550 

"Power"  efficiency,  in  per  cent,  (at 

rated  load)       

97,1 

97,2 

97,3 

"Energy"  efficiency,  in  per  cent.,  for 

load  factor  of  0,20    . 

93,1 

93,2 

93,9 

Some  of  the  important  differences  in  the  designs,  of  which 
the  leading  data  are  given  in  Table  11,  are  brought  together 
in  Table  12.  The  most  striking  difference  is  in  the  weights. 
The  general  outline  drawings  of  the  three  designs  are  shown  in 
Figs.  53,  54  and  55.  These  figures  show  very  clearly  the 
influence  of  the  periodicity  upon  the  relative  proportions  of 
the  transformer. 

TABLE  12. — SHOWING  THE  INFLUENCE  OF  THE  PERIODICITY  UPON  THE 
CORE  Loss,  WEIGHTS,  ETC.,  OF  20-KvA  TRANSFORMERS. 


Periodicity 
(in  cycles 
per  sec). 

Core  loss 
(in  watts). 

Weight  of 
active  material 
per  leva 
(in  kg). 

"  Power  " 
efficiency  at 
full  load  (in 
per  cent.). 

No-load 
current  (in 
per  cent,  of 
full  load 
current). 

No-load 
power  factor. 

15 

230 

21,3 

97,15 

12,0 

0,098 

25 

214 

12,6 

97,23 

9,0 

0,115 

50 

190 

7,2 

97,34 

4,4 

0,22 

These  three  designs  have  been  prepared  on  the  basis  of  the 
same  I2  H  loss  for  all  periodicities.  So  wide  is  the  range  of 
choice  of  assumptions  on  which  comparisons  of  this  sort  may 
be  based,  that  the  results  obtained  must  always  be  considered 
with  an  open  mind  and  with  a  clear  recognition  of  the  impossi- 
bility of  establishing  any  absolutely  general  comparison. 


92      THE   DESIGN   OF    STATIC   TRANSFORMERS 


CHAPTER  VII 

THE  EEGULATION  OF  TRANSFORMERS 

OUR  20-kva  transformer  has  3100  primary  turns  and  124 

O-J  A  A          \ 

=  )  25. 


If  a  pressure  of  5000  volts  be  applied  at  the  terminals  of 
the  primary  winding,  and  if  the  secondary  winding  is  on  open 
circuit,  i.e.,  if  the  transformer  is  in  circuit  but  unloaded,  then 
the  pressure  at  the  terminals  of  the  secondary  winding  will  be 


'-sjr  —    200  volts.    If  the  secondary  circuit  be  closed  through 

an  impedance,  then  current  will  flow  from  the  secondary  wind- 
ing into  this  external  secondary  circuit  and  the  pressure  at  the 
secondary  terminals  will  decrease  below  200  volts  (except  in 
the  unusual  case  that  the  current  flowing  into  the  external 
secondary  circuit  is  leading).1  The  percentage  by  which  the 
secondary  terminal  pressure  falls  below  the  value  correspond- 
ing to  no  load  (in  this  case  200  volts)  is  termed  the  "regulation  " 
corresponding  to  the  load  in  question.  If  the  pressure  has 
fallen  to  196  volts,  then,  for  the  corresponding  load,  the  regula- 

tion is  said  to  be  (20°2~0196  X  100  =)  2,0  per  cent.    The  fall 

in  pressure  is  greater  the  greater  the  current  flowing  and  the 
lower  the  value  of  6r(the  power  factor  of  the  external  circuit). 
If,  without  any  accompanying  statement  as  to  load  and  power 
factor,  it  is  stated  that  the  regulation  of  a  transformer  is,  say, 
1,5  per  cent.,  this  is  usually  intended  to  mean  that  when  the 
transformer  is  delivering  its  rated  load  to  a  non-inductive 

1  For  a  given  transformer  there  will,  for  any  given  value  of  the  secondary 
current,  be  some  particular  angle  of  lead  above  which  the  terminal  pressure  will 
be  greater  when  this  current  flows  than  on  open  circuit. 


94      THE   DESIGN   OF   STATIC   TRANSFOKMERS 

circuit  (G  =  1,00)  the  pressure  at  the  secondary  terminals 
will  be  1,5  per  cent,  lower  than  at  no  load. 

The  drop  in  pressure  is  due  to  two  causes,  (1)  the  resistance 
of  the  windings,  and  (2)  the  inductance  of  the  windings.  The 
more  the  primary  and  the  secondary  windings  are  intermixed 
with  one  another,  the  less  will  be  the  second  component 
(i.e.,  the  inductance  of  the  windings).  It  is,  however,  for 
obvious  practical  reasons,  chief  amongst  which  is  the  import- 
ance of  having  excellent  insulation,  not  feasible  to  go  very  far 
in  the  direction  of  intermixing  the  primary  and  secondary 
windings.  The  inductanee  is  greater  the  lower  the  magnetic 


FIG.  56. — Diagram  showing  magnetic  leakage  in  core-type  transformer. 

reluctance  of  the  path  offered  to  the  passage  of  magnetic  flux 
between  the  primary  and  secondary.  This  flux  is  termed  the 
leakage  flux.  To  keep  down  the  inductance  it  is  important 
that  as  much  as  possible  of  the  magnetic  flux  shall  be  linked 
both  with  the  primary  and  secondary  windings,  i.e.,  it  is 
important  that  the  magnetic  flux  shall  be  restricted  to  the 
main  magnetic  circuit,  so  far  as  practicable. 

In  Fig.  56  the  coil  marked  P  represents  the  primary  and 
the  coil  marked  S  represents  the  secondar}r.  When  the 
secondary  is  delivering  electricity  to  an  external  circuit,  the 
current  in  its  windings  flows  in  the  opposite  direction  to  that 
of  the  current  in  the  primary  windings.  Consequently  if  we 
consider  the  conductors  lying  within  the  winding  window,  we 


THE   REGULATION   OF   TRANSFORMERS  *      95 


shall  find  the  primary  current  flowing,  say,  from  front  to  back, 
as  in  the  diagram  in  Fig.  56,  while  the  secondary  current  flows 
from  back  to  front.  It  is  thus  clear  that  the  conductors  will 
co-operate  to  setup  a  leakage  flux  (as  shown  in  the  diagram) 
across  the  winding  window  from  the  top  portion  of  the  core 
represented  in  Fig.  56  to  the  bottom  portion.  The  core  and 
windings  in  Fig.  56  are  arranged  in  a  very  unfavourable  way  so 
far  as  relates  to  minimising  the  magnetic  leakage.  By  such  a 


FIG.  57. — Diagram  showing  magnetic  leakage  in 
core-type  transformer. 

re-arrangement  as  that  shown  in  Fig.  57,  where  the  coils  are 
wound  on  the  long  sides  of  the  core,  the  leakage  path  is  much 
longer  and  is  consequently  of  much  higher  magnetic  reluctance, 
and  the  leakage  flux  will  consequently  be  less.  But  as  regards 
magnetic  leakage,  the  arrangement  shown  in  Fig.  57  is  still 
very  bad.  The  reader  will  now  be  better  able  to  appreciate 
one  of  the  chief  advantages  of  employing  magnetic  circuits  of 
the  general  proportions  of  that  already  shown  in  Fig.  36  on 
p.  58.  The  longer  and  narrower  the  winding  window,  the 
greater  will  be  the  reluctance  of  the  magnetic  path  for  the 


96      THE   DESIGN   OF   STATIC   TKANSFOBMEKS 

leakage  flux.  But  even  in  such  a  case  as  that  of  Fig.  36,  it 
would  not  suffice  to  have  the  primary  windings  occupy  one  of 
the  vertical  legs  and  the  secondary  windings  the  other.  Such 
an  arrangement  would  still  afford  far  too  great  a  cross-section 
for  the  leakage  flux  between  the  primary  and  secondary  wind- 
ings. But  hy  winding  the  secondary  the  full  length  of  each 
vertical  leg  and  by  arranging  the  primary  coils  immediately  over 
the  secondary  coils,  as  shown  in  Figs.  49  and  50,  on  pp.  82  and 
83,  only  leaving  enough  room  between  them  to  ensure  effective 
insulation,  the  opportunity  for  leakage  flux  to  pass  between 
primar}^  and  secondary  is  much  reduced.  Moreover  by  having 
the  windings  shallow  we  keep  down  the  magnetomotive  force 
per  centimeter  of  length  of  winding  window,  and  since  the 
leakage  flux  is  proportional  to  this  specific  mmf,  the  use  of  these 
shallow  windings  is  in  the  interests  of  low  inductance.  For 
such  a  case  as  our  20-kva  transformer,  the  simple  concentric 
arrangement  shown  in  Fig.  30,  on  p.  51,  and  in  Figs.  53,  54 
and  55,  on  p.  92,  with  the  secondary  wound  inside  and  the 
primary  outside  on  each  vertical  leg,  leads  to  a  sufficiently  low 
inductance,  but  cases  often  arise  where  a  triple-concentric 
arrangement,  such  as  that  indicated  in  Fig.  31,  on  p.  51,  must 
be  employed  in  order  to  obtain  the  required  low  inductance  and 
close  regulation.  The  sandwich  winding  of  Fig.  32,  p.  52,  may 
also  lead  to  low  inductance  and  close  regulation  if  the  sub- 
division is  carried  far  enough,  but  when  this  arrangement  is 
employed  with  a  long  and  narrow  winding  space,  it  must  be  kept 
in  mind  that  the  length  of  the  leakage  path  from  one  side  of  the 
narrow  winding  space  to  the  other,  is  very  low,  and  this  in  itself 
tends  to  low  magnetic  reluctance  of  the  leakage  pjath  between 
the  primary  and  secondary  windings. 

Other  things  being  equal,  the  inductance  will  obviously  be 
less  the  higher  the  magnetic  density  employed  in  the  core,  for 
this  will  tend  toward  minimising  the  mean  length  of  both 
primary  and  secondary  turns  and  consequently  will  reduce  the 
cross-section  of  the  leakage  path. 


THE   REGULATION   OF   TRANSFORMERS         97 

The  higher  the  inductance  of  a  transformer,  the  greater  will 
be  the  pressure  which  will  be  required  at  the  primary  terminals 
to  send  a  given  current  through  the  secondary  winding  when 
the  latter  is  short-circuited.  Consider  a  100-kw  transformer 
wound  for  3000  primary  volts  and  200  secondary  volts.  The 


ratio  of  transformation  is  I  T^TT  —  )  15.    Its  secondary  current, 

at  its    rated    load    of    100    kw,  is    (for    unity    power-factor) 

(1 00  000  \ 
—  =)  500  amperes.  If  the  secondary  is  short- 
circuited  through  an  ammeter,  and  if  the  pressure  at  the 
primary  terminals  is  gradually  raised,  then,  for  a  reasonably 
good  design,  it  may  be  found  that  it  will  require  a  pressure  of, 
say,  100  volts  at  the  primary  terminals  to  send  the  full-load 
current  of  500  amperes  through  the  short-circuited  secondary. 

The  corresponding  primary  current  is  \-=-g  =J  33,3  amperes. 
The  "impedance  "  of  the  transformer  under  these  conditions 

may  be  said  to  be  f  ^  =-5  =±1  3,3  ohms.     The  impedance  is 
v  00,0      / 

made  up  of  two  components,  the  resistance  and  the  reactance.1 
As  reasonable  values  for  the  resistances  of  the  primary  and 
secondary  windings  of  this  100-kw  transformer,  we  may  take 
0,60  ohm  and  0,0020  ohm  respectively.  It  is  convenient  at 
certain  steps  in  transformer  calculations  to  reduce  the  data  to 
an  "  equivalent "  transformer,  but  with  a  1:1  ratio  of  trans- 
formation. Thus  our  100-kw  transformer,  for  3000  primary 
and  200  secondary  volts  and  a  ratio,  of  transformation  of  15, 
can  be  replaced  by  an  "  equivalent "  transformer  for  100  kw,  but 
with  both  primary  and  secondary  coils  wound  for  3000  volts. 
For  this  "  equivalent "  transformer  we  should  still  have  the 
resistance  of  the  primary  winding  equal  to  0,60  ohm  as 

1  Impedance  and  reactance  are  dealt  with  in  a  non-mathematical  manner  in 
a  little  treatise  by  the  author,  entitled  "  Electricity,"  and  published  in  1910  by 
Messrs.  Constable,  London. 

S.T.  H 


98      THE   DESIGN   OF   STATIC   TRANSFORMERS 

before,  but  the  resistance  of  the  secondary  winding  would 
now  be 

152  X  0,0020  =  0,45  ohm. 

Instead  of  dealing  separately  with  the  resistance  of  the  primary 
and  the  resistance  of  the  seconda^,  we  may,  for  such  a  1  :  1 
transformer,  speak  of  the  "  resistance  of  the  transformer"  and 
say  that  it  is  equal  to 

0,60  +  0,45  =  1,05  ohm. 

The  "  resistance  drop  "  in  this  transformer,  when  the  input  is 
33,3  amperes,  is 

1,05  X  33,3  =  35  volts. 

The  100  volts  which  we  have  stated  to  be  necessary  to  send 
full-load  current  into  the  transformer  when  the  secondary  is 
short-circuited,  is  made  up  of  two  components.  One  compo- 
nent is  the  "resistance  drop  "  of  35  volts,  which  we  have  just 
calculated.  The  other  component  is  the  "  reactance  drop," 
and  is  equal  to 

VlOO2  -  352  =  94  volts. 

In  the  example  we  have  taken,  we  should  say  that  for  a  primary 
current  of  33,3  amperes,  the  "  resistance  drop  "  is 

35 

X  100  =  1,17  per  cent. 


and  the  "reactance  drop"  is 
04 


x  10°  =  3-1  pfir  cent- 

The  resistance  drop  is  simply  calculated  from  the  number  of 
turns,  the  cross-section  and  the  mean  length  of  turn  in  the 
primary  and  secondary  windings.  Such  calculations  have 
already  been  carried  through  step  by  step  in  Chapter  II. 

The  reactance  drop  can  only  be  very  roughly  estimated.  It 
varies  greatly  with  different  types  of  magnetic  circuit,  with 
different  proportions  of  the  winding-space  and  with  different 
arrangements  of  the  winding. 


THE   EEGULATION   OF   TKANSFORMEKS         99 

In  1896  I  devised  a  method  of  estimating  the  reactance 
drop  of  a  core-type  transformer  with  concentric  windings  and 
an  elongated  winding-space,  and  I  have  used  it  with  good 
results  during  the  last  fourteen  years.  The  method  is  based 
on  the  following  formula  : — 

percentage  reactance  drop  =/-7   v 

U    /\    C 

f  =  a  factor  depending  upon  the  width  of  the  winding  window, 

the  depth  of  the  windings,  the  number  of  concentric  windings 

employed  and  the  thickness  of  the  insulation  or  of  the  air  or 

oil  space  between  the  primary  and  secondary  windings. 

a  =  virtual  (i.e.,  rrns)  value  of  the   primary  ampere-turns  at 

rated  load. 

I)  =  height  of  winding  space  in  cm. 

c  =•  core  density  in  kilolines  per  sq  cm. 

For  a  single  concentric  winding,  i.e.,  for  a  winding  of  the 
type  employed  in  our  20-kva  transformer  (see  also  Fig.  30)  > 
the  values  for  /  range  from  0,05  to  0,12,  being  higher  the 
greater  the  depth  of  the  coils.  For  triple-concentric  windings 
(see  Fig.  31)  the  range  of  values  for  /  is  from  0,03  to  0,07. 
For  still  greater  subdivision  of  the  winding,  lower  values 
must  be  used  for  /.  For  more  definite  values,  each  designer 
will  acquire  his  own  experience,  recording  the  results  observed 
on  test  and  working  back  to  the  factor  /.  For  single-con- 
centric windings  the  curve  in  Fig.  58  may  be  found  useful  in 
obtaining  values  for  /.  Our  20-kva  design  has  decidedly 
shallow  coils  and  a  narrow  winding  window.  It  is  for  only 
moderate  pressure  (5000  volts),  and  the  primary  and  secondary 
coils  come  quite  close  up  to  one  another  (as  shown  in  Fig.  50, 
on  p.  83).  It  will  be  appropriate  in  this  case  to  take 

/  =  0,080. 

The  primary  winding  has  3100  turns,  and  the  input  at  rated 
load  is  4,12    amperes.       Consequently  for    "  a,"    the   virtual 
value  of  the  primary  ampere-turns,  we  have 
a  =  4,12  X  3100  =  12800. 

H2 


100     THE   DESIGN   OF    STATIC   TRANSFOKMEBS 


The  height  of  the  winding  space  ("  I  "  in  the  formula)  is  51. 
The  core  density  ("  c  "  in  the  formula)  is  11,5  kilolines  per 
sq  cm.  Substituting  these  values  in  the  formula,  we 
obtain 

12800 
>1  X  11,5  -  1J5' 


Percentage  reactance  drop  =  0,080 


0.2Z 


^ 


O.t 


.0.5 


0.6 


Q2.  O.J  0* 

of  Width  of   V/indow  to  Lenyfh   of 
FIG.  58.  —  Curve  of  values  for  /  in  formula  "  percentage  reactance 
drop  =  /  £.» 

We  have  already  seen  that  the  resistance  drop  is  equal  to  1,80 
per  cent.     Thus  we  have 

Eeactance  drop  =  0,0175  X  5000  =  87,6  volts 
Eesistance  drop  =  0,0180  X  5000  =  90,0  volts 
Impedance  Voltage  ==  A/87,62  +  90,02  =  125  volts. 


THE   EEGULATION   OF   TRANSFORMERS       101 

The  result  indicates  that  in  order  to  send  full-load  current  of 
100  amperes  through  the  short-circuited  secondary  of  our 
20-kva  transformer,  a  primary  pressure  of  125  volts  will  be 
required. 

Let  us  study  the  influence  of  the  two  component  drops  on 
the  regulation  of  a  transformer.  In  actual  practice  these 
components  constitute  but  a  very  small  percentage  of  the 
terminal  pressure,  but  for  our  examination  of  the  subject,  it 
will  be  preferable  to  take  a  case  in  which  the  component  drops 
are  quite  considerable.  Let  the  transformer  have  a  1  : 1  ratio  of 
transformation  and  let  the  secondary  pressure  be  100  volts  at 
no  load.  Then  at  no  load  the  primary  pressure  will  also  be 


//5 


3 


FIG.  59. — Transformer  diagram  with  no  reactance,  but  with  an  I  R  drop  of 

15  per  cent. 

100  volts.    Let  the  resistance  drop  at  full  load  be  15  per  cent, 
of  the  secondary  pressure. 

If  the  transformer  had  no  reactance  drop,  then  in  order 
to  have,  at  full  load  and  unity  power  factor,  a  pressure  of  100 
volts  at  the  terminals  of  the  secondary  winding,  it  would  be 
necessary  to  apply  a  pressure  of  115  volts  at  the  terminals  of 
the  primary  winding.  Or  if  at  all  loads  we  maintain  a  con- 
stant pressure  of  115  volts  at  the  terminals  of  the  primary 
winding,  then  as  the  load  is  increased  the  pressure  at  the 
terminals  of  the  secondary  winding  (which  is  115  volts  at  no 
load)  will  gradually  decrease  until  at  full  load  the  secondary 
pressure  will  only  be  100  volts.  This  is  shown  diagrammatically 
in  Fig.  59.  If,  instead  of  having  a  negligible  reactance  drop 
at  full  load,  there  is,  in  addition  to  the  resistance  drop  of 
15  volts,  also  a  reactance  drop  of  30  volts,  then  (for  unity 
power  factor  of  the  external  circuit  supplied  from  the 


102     THE   DESIGN   OF    STATIC   TRANSFORMERS 

secondary)  the  diagram  will  be  modified,  as  shown  in  Fig.  60? 
and  we  see  that  a  primary  pressure  of  119  volts  is  necessary 


FIG-.  60. — Transformer  diagram  with  30  per  cent,  reactance  drop  and  15  percent. 
/  R  drop.     Power  factor  =  unity. 


FIG.  61. — Transformer  diagram  with  30  per  cent,  reactance  drop  and  15  per 
cent.  I R  drop.     Angle  of  lag  <J>  =  30°.     Cos  4>  =  0,886. 

in  order  that  we  may,  at  full  load,  obtain  100  volts  at  the 
secondary  terminals  ;  in  other  words,  the  pressure  at  the 
secondary  terminals  will  gradually  fall  from  119  volts  at  no  load 
to  100  volts  at  full  load. 


THE   BEGULATION   OF   TBANSFOKMEKS       103 


The  diagram  in  Fig.  61  shows  the  construction  which 
should  be  employed  when  the  power  factor  of  the  circuit 
supplied  by  the  secondary  is  less  than  unity,  and  the  current 
lags  behind  the  terminal  pressure.  In  the  case  illustrated, 
C  B  represents  the 
secondary  terminal  A  /$ 
pressure  of  100  volts. 
The  current  lags  behind 
the  pressure  by  30°. 
Since  cos  30°  =  0,886, 
the  power  factor  of  the 
circuit  supplied  from 
the  secondary  is  0,886 
(G  -  0,886).  The 
vector  C  E  indicates 
the  direction  of  the 
secondary  current,  and 
is  30°  behind  C  B,  the 
vector  representing  the 
secondary  terminal 
pressure.  In  Figs.  59 
and  60  the  single  vector 
C  B  represented  the 
phase  of  the  secondary 
terminal  pressure  and 
also  the  phase  of  the 
secondary  current 
which  was  in  phase  with 
the  pressure.  C  D  of 
Fig  61  represents  the 


•Transformer  diagram  with  30   per 
cent,  reactance  drop  and  15  per  cent.  I R 


FiG.   62. 

.  reactance  drop  and 
drop.  Angle  of  lag  <J>  =  63°.   Cos  $  =  0,  440. 


reactance  drop  of  30  volts  at  rated  load,  and  is  90°  in  phase 
behind  the  vector  C  E  representing  the  current.  The  resistance 
drop  is  represented,  as  in  Fig.  60,  by  a  vector  A  D,  which  has 
the  same  direction  as  (i.e.,  is  parallel  to)  the  vector  C  E  repre- 
senting the  current.  The  primary  pressure  is  represented  in 


104     THE  DESIGN  OF   STATIC  TRANSFORMERS 

phase  and  magnitude  by  the  vector  A  B,  and  is  seen  to  be 
equal  to  129  volts  when,  as  in  Fig.  61,  G  is  equal  to  0,886. 
In  Fig.  62  we  arrive  at  the  value  of  G  corresponding  to  the 


FIG.  63. — Transformer  diagram 
with  30  per  cent,  reactance 
drop  and  15  per  cent.  I R 
drop.  Angle  of  lag  <p  =  78°. 
Cos  $  =  0.21. 


FIG.  64. — Transformer  diagram 
with  30  per  cent,  react- 
ance drop  and  15  per  cent. 
/  R  drop.  Angle  of  lag 

#  =  90°.    Cos  $  =  0. 


maximum  drop.  This  always  occurs  when  the  tangent  of  the 
angle  of  lag  of  the  secondary  current  behind  the  secondary 
pressure  is  equal  to  the  ratio  of  the  reactance  drop  to  the 
resistance  drop,  i.e.,  for  the  condition 


BE  :C  E  =  C  D  :AD. 


THE   REGULATION   OF   TRANSFORMERS       105 


For  the  example  we  are  employing,  this  occurs  for  G  =  0,44. 
For  still  lower  power  factors  of  the  external  secondary  circuit, 
the  pressure  drop  again  decreases,  as  will  be  seen  by  a  study 
of  Figs.  63  and  64,  the  latter  representing  the  limiting  case  of 
90°  lag.  In  Fig.  65  the  values  of  the  drop  are  plotted  in  two 
curves — in  the  one  the  drop  is  plotted  as  a  function  of  the  power 

J'0 


•s* 

I 

v    30 


25 
20 
/5 
/O 


O,Z     Q3     Q4-    Q5    Q6    Q?    O,8    Q9    /,O 
foner  factor  of  &econd#ry  Load 


/O      2Q      3O    4O      JO     &>     70      GO     &0 
&eg.  /<ag  o/  £>eccnd#ry,   Current   Behind 

FIG.  65. — Variation  of  drop  with  power  factor  and  angle  of  lag. 

factor  of  the  external  secondary  circuit,  and  in  the  other  the 
drop  is  plotted  as  a  function  of  the  angle  of  lag'of  the  secondary 
current  behind  the  secondary  terminal  pressure.  It  is  seen 
that  the  drop  at  first  increases  with  decreasing  power  factor, 
reaches  a  maximum  and  then  decreases.  The  method  and 
diagrams  in  Figs.  59  to  65  were  worked  out  b}^  the,  author  in 
1895.  It  is  not  usual  (as  shown  in  these  diagrams  and  in 
Fig.  65)  to  designate  as  the  regulation  the  percentage  which 


106     THE   DESIGN   OF    STATIC   TRANSFORMERS 

the  drop  in  volts  from  no  load  to  full  load  constitutes  of  the 
secondary  pressure  at  full  load,  hut  rather  the  percentage  which 
it  hears  to  the  secondary  pressure  at  no  load,  the  primary 
pressure  being  assumed  to  be  maintained  constant  as  the  load 
increases.  Nevertheless,  since  the  author  originally  worked 


FIG.  66.— Kegulation  diagram  of  20-kva  5000/200-volt  50-cycle 
single-phase  transformer. 

out  the  diagrams  in  the  former  way,  it  has  been  to  him  a 
matter  of  interest  to  preserve  them  unchanged,  and  it  is  not 
apparent  that  the  principles  involved  are  thereby  rendered  any 
less  clear. 

Keturning  to  the  case  of  our  20-kva  transformer,  we  have 
seen  on  p.  100  that  the  reactance  drop  is  87,6  volts  and  the 


THE   KEGULATION   OF   TRANSFORMERS       107 

resistance  drop  90,0  volts.  In  Fig.  66  (which  is  based  on  a 
diagram  devised  by  Kapp  l)  A  D  and  D  C  are  drawn  to  scale, 
and  are  respectively  proportional  to  87,6  and  90,0.  With  A 
as  a  centre,  and  a  radius  proportional  to  5000  (the  constant 
primary  pressure),  the  arc  Bo  BQO  is  drawn.  Radiating  from  C 
are  drawn  lines  representing  the  phase  of  the  secondary  terminal 
pressure  for  various  power  factors.  These  lines  intersect  the 
arc  BQ  BQO  at  various  points,  B0)  BIO,  B^o,  etc.,  the  subscripts 
denoting  the  angle  by  which  the  vector  C  BO,  representing  the 
secondary  current,  lags  behind  the  secondary  terminal  pressure. 
The  lengths  of  the  lines  C  B0,  C  BIO,  C  B^o,  etc.,  are  propor- 
tional to  the  secondary  terminal  pressure  for  the  case  of  an 
equivalent  transformer  with  a  1:1  ratio  of  transformation.  The 
actual  secondary  terminal  pressures  for  these  conditions  of  load, 
and  for  the  constant  primary  pressure  of  5000  volts,  may  be 
found  by  dividing  these  results  by  25,  the  ratio  of  transforma- 
tion of  the  actual  transformer.  It  is  seen  from  the  diagram 
that  the  regulation  lies  between  1,70  per  cent,  and  2,56  per 
cent,  according  to  the  power  factor  of  the  external  circuit 
supplied  by  the  secondary. 

Kapp's  Modified  Diagram  of  Drop. — The  graphical  method 
of  estimating  the  regulation  at  various  power  factors,  as  shown 
in  Fig.  66,  suffers  from  the  disadvantage  that  in  practice  the 
distance  representing  the  drop  is  generally  very  small  in  com- 
parison with  the  radii  of  the  circle,  so  that  an  accurate  deter- 
mination of  the  drop  by  a  purely  graphical  method  becomes 
impracticable.  If,  however,  A  D  and  D  C  (Fig.  66)  are  very 
small  compared  with  C  BIO,  C  B2o,  etc.,  then  Kapp2  has  shown 
that  it  becomes  practicable  to  simplify  the  diagram,  without 
introducing  appreciable  error. 

He  thus  avoids  the  difficulty  above-mentioned.  The  method 
will  be  explained  by  reference  to  Figs.  66  and  67.  If  in 
Fig.  66  a  line  is  drawn  joining  A  and  BIO,  then  this  will  be 

1  "  Transformers,"  2nd  edition,  1908,  p.  172. 

2  "  Transformers,"  2nd  edition,  1908,  p.  174, 


108     THE   DESIGN   OF    STATIC   TRANSFORMERS 

nearly  parallel  to  C  BIO,  and  if  (as  in  Fig.  67)  a  perpendicular 
is  dropped  from  C  intersecting  A  BIQ  at  Ew,  then  A  EIQ  will 
be  equal  very  nearly  to  the  actual  drop  at  the  power  factor 
represented  by  the  radius  C  BIQ,  i.e.)  at  a  power  factor  of  0,98. 


90 


FlG.  67. — Modified  regulation  diagram  of  20-kva  5000/200-volt  single-phase 

transformer. 

The  diagram  may  thus  be  conveniently  drawn  to  a  large  scale, 
as  shown  in  Fig.  67,  thereby  eliminating  to  a  large  extent 
inaccuracy  in  drawing  and  scaling  off  the  diagram.  In  Fig.  67 
A  D  represents  the  resistance  drop  andD  C  the  inductive  drop. 
A  BIQ  is  drawn  parallel  to  C  BIQ,  which  makes  an  angle  of  lag  of 
10°  with  C  BQ.  A  line  C  EIQ  is  drawn  perpendicular_to  A  BIQ. 


THE   EEGULATION   OF   TRANSFORMERS       109 


We  thus  obtain  A  EIQ,  which  represents  the  drop.  It  will  at 
once  be  obvious  that  the  points  EIQ,  E^Q,  etc.,  will  lie  upon  the 
circumference  of  a  circle  whose  diameter  is  equal  to  A  C  (i.e., 
to  the  impedance  drop),  and  whose  centre  lies  midway  between 
A  and  C.  The  drop  at  various  angles  of  lag  will  be  repre- 
sented by  the  chords  A  EIQ,  A  E2o,  etc.,  of  this  circle.  Com- 


0,3      0.4      Q5     Q6      C,J 
factor  of  £xter/w 

FIG.  68.— Regulation  curves  of  20-kva  5000/200-volt  single-phase  transformer. 

paring  this  diagram  with  that  in  Fig.  66  it  will  be  observed 
that  the  modified  diagram  is  more  inaccurate  at  high  and  low 
power  factors  of  the  external  circuit,  and  that  between  power 
factors  of  0,5  and  0,95  (for  the  particular  example  taken),  the 
inaccuracy  is  very  small.  The  results  obtained  respectively 
from  Figs.  66  and  67  are  compared  in  the  curves  in  Fig.  68, 
the  broken  line  curve  representing  the  results  obtained  from 
Fig.  67,  and  the  full  line  curve  the  original  results  obtained 
by  means  of  Fig.  66.  The  inaccuracy  introduced  by  Fig.  67 
will  be  smaller  the  smaller  the  resistance  drop  and  the 
reactance  drop  are  as  compared  with  the  terminal  pressure. 


110     THE   DESIGN   OF    STATIC   TRANSFOEMERS 

REGULATION     OF     TRANSFORMERS     FOR     THREE-WIRE 
SECONDARY    CIRCUITS 

The  majority  of  core-type  transformers  used  for  lighting 
purposes  have  windings  of  the  concentric  type,  i.e.,  the  primary 
is  wound  over  the  secondary,  or  vice  versa,  and  primary  and 
secondary  each  consist  of  long  cylindrical  coils.  The  simple 
concentric  type  (see  Fig.  30  on  p.  51)  consists  of  two  coils  per 
leg,  the  primary  usually  being  wound  over  the  secondary  ;  the 
triple-concentric  type  (see  Fig.  31  on  p.  51)  consists  of  three 
coils  per  leg.  Two  of  these  three  coils  may  constitute  the 
secondary,  the  primary  coil  being  wound  in  between  these  two 
secondary  coils.  When  using  a  transformer  on  a  three-wire 
secondary  circuit,  it  is  necessary  to  provide  two  separate 
groups  of  secondary  coils,  each  group  of  coils  giving  the  same 
pressure.  At  first  sight,  the  most  obvious  way  of  connecting  a 
transformer  of  the  core  type  to  supply  a  three-wire  secondary 
circuit  would  appear  to  be  to  utilise  the  secondary  coils  on  one 
leg  of  the  transformer  for  one  side  of  the  three-wire  circuit,  and 
the  secondary  coils  on  the  other  leg  for  the  other  side  of  the 
three-wire  circuit.  With  these  connections,  equal  pressures 
would  be  obtained  from  both  secondaries  provided  they  were 
equally  loaded  ;  but  if  the  two  secondaries  are  not  equally 
loaded  it  is  evident  that  the  transformer  will  regulate  badly, 
the  pressure  of  the  side  on  which  the  greater  load  exists  being 
below  normal,  while  the  pressure  of  the  lightly  loaded  side  will 
rise  above  normal,  the  sum  of  the  pressures  on  the  two  sides 
remaining  constant,  whatever  the  distribution  of  the  load. 
That  this  must  be  the  case  may  be  explained  as  follows  : — 

Consider  one  side  of  the  three-wire  system  to  be  unloaded 
and  the  other  side  to  be  fully  loaded.  If  both  the  primary 
windings  are  connected  in  series,  the  same  primary  current 
must  flow  in  all  parts.  One-half  of  the  primary  ampere  turns 
will  be  on  that  leg  of  the  transformer  whose  secondary  is 
loaded,  and  the  other  half  will  be  on  the  leg  with  the  unloaded 


THE   REGULATION   OF   TRANSFORMERS      111 


FlG.  69. — Arrangement  of  coils 
in  core-type  transformer  for 
three- wire  secondary. 


secondary.     The  first  part  of  this  chapter  dealt  with  magnetic 
leakage,  and  it  was  shown  that  for  close  regulation  the  primary 
and  secondary  coils  must  be  close 
together     and     intermixed.        If, 
therefore,   the    pressure    on    one 
side  of  the   three-wire  system   is 
provided  by   a  secondary  coil  on 
one  leg,  and  the  pressure  on  the 
other  side  by  a  secondary  coil  on 
the  other  leg,  and  if  only  one  of 
these  coils  be  loaded,  there   will 
be    a   large    leakage   flux   caused 
by  the  ampere  turns  of  that  part 
of    the    primary    winding    which 
is     wound     on     that   leg    whose 
secondary  is  unloaded.     For   full  load   on   one    side   and  no 
load  on  the  other  side  of  the  three-wire  system,  this  may  easily 
result  in  a   rise  of  as 
much  as  25  per   cent, 
in  the  pressure  on  the 
unloaded  side,    and   a 
drop  of  25  per  cent,  in 
the    pressure    on    the 
loaded     side,    making 
the  pressure  across  the 
unloaded    side  greatly 
exceed     that    on     the 
loaded  side.    This  was 
first  pointed    out    and 
investigated     by     Mr. 
W.    S.    Moody.      The 
inequality  in  the  mag- 
netic  leakage    may   be   prevented   by    adopting    connections 
(originally    suggested   by   Mr.  Moody)  which  distribute  both 
halves    of  the   secondary  winding  equally  over  the   two  legs. 


FIG.  70.— Arrangement  of  coils  in  core-type 
transformer  for  three-wire  secondary. 


112     THE   DESIGN   OF    STATIC   TRANSFORMERS 


3fS 


This  may  be  done  by  splitting  the  coil  up  as  shown  in  Fig.  69 
and  connecting  the   primaries  in    series,  the   secondary   coils 

Si  and  83  being  connected  in 
series  for  one  side  of  the  three- 
wire  system  and  $2  and  S±  for 
the  other  side  ;  or  else  Si  and 
S±  may  (as  indicated  in  Fig.  70) 
be  connected  in  series  for  one 
side,  and  S%  and  $3  for  the  other 
side. 

Where  the  primary  winding  is 
interposed  between  two  second- 
aries as  shown  in  Fig.  71,  it 
becomes  practicable  to  remedy 
the  unbalancing  by  connecting 
Si  and  $4  in  series  on  one  side  and  $2  and  83  in  series  on  the 
other  side  of  the  three-wire  system,  i.e.,  to  connect  the  outside 
secondary  coil  on  one  leg,  in  series  with  the  inside  secondary 
on  the  other  leg,  as  this  tends  to  ensure  the  exact  equality  of 
resistance  and  reactance  in  the  two  halves. 


FIG.  71. — Arrangement  of  coils 
in  core-type  transformer  for 
three-wire  secondary. 


CHAPTER  VIII 

THE    HEATING   OF   TRANSFORMERS 

ALTHOUGH  the  efficiencies  of  static  transformers  are  generally 
high  and  the  losses  consequently  small,  nevertheless,  owing 
to  the  absence  of  any  ventilating  effects  from  moving  parts,  the 
problem  of  limiting  the  temperature  rise  is  one  of  considerable 
difficulty.  The  difficulties  encountered  are  greater  the  greater 
the  rated  capacity  of  the  transformer.  In  the  early  days  when 
the  demand  for  transformers  was  confined  to  small  sizes,  the 
problem  of  limiting  the  temperature  rise  would  hardly  have 
arisen  except  for  the  fact  that  the  material  employed  for  the 
magnetic  circuit  was  at  that  time  very  poor  and  the  losses  in 
it  were  high.  If  the  active  material  in  a  transformer  only 
amounts  to  some  two  or  three  KILOGRAMS,  the  surface  per 
kilogram  of  material  will,  with  ordinary  forms,  be  far  greater 
than  in  a  transformer  containing  two  or  three  TONS  of  active 
material ;  and  consequently  while  in  the  former  size  it  suffices 
that  the  transformer  need  simply  be  surrounded  by  air,  and 
will  be  maintained  cool  by  natural  processes  of  heat  emission, 
it  becomes  necessary  in  the  latter  case  to  resort  to  additional 
means,  such  as  immersing  the  transformer  in  a  tank  of  oil  and 
abstracting  the  heat  from  the  oil  and  its  contents  by  the 
circulation  of  water  through  pipes  immersed  in  the  oil. 

In  Fig.  72  is  shown  a  design  for  an  air-cooled  transformer 
in  which  the  emission  of  heat  from  the  active  material  is  very 
appreciably  increased  by  the  various  ways  in  which  additional 
surface  is  provided.  The  windings  are  sub-divided  into  a 
number  of  small  coils,  and  cooling  ribs  of  sheet  copper  about 
0,5  mm.  thick  are  arranged  between  adjacent  coils.  It  will  be 
seen  that  the  core  is  also  of  such  a  shape  as  to  have  a  large 

S.T.  i 


114     THE   DESIGN   OF   STATIC   TRANSFORMERS 


FIG.  72. — Air-cooled  transformer. 


THE   HEATING   OF   TEANSFOKMEES          115 

cooling  surface.  Some  tests  are  reported  to  have  been  made 
on  a  5,5-kw  transformer  of  this  type 'in  comparison  with  an 
ordinary  transformer  of  the  same  size.  The  transformers  were 
operated  for  a  sufficient  length  of  time  to  obtain  the  ultimate 
temperature  rise.  In  the  transformer  without  the  ribs  this 
occurred  after  eight  or  nine  hours,  and  in  a  somewhat  shorter 
time  in  the  ribbed  transformer.  It  is  stated  that  it  was  found 
that  the  construction  permitted  of  rating  the  transformer  at 
twice  as  great  a  load  as  could,  for  the  same  temperature  rise,  be 
obtained  by  the  ordinary  construction,  and  that  for  a  given  total 
loss  the  temperature  rise  of  both  copper  and  iron  is  halved  by 
the  use  of  the  ribbed  construction.  It  is  further  claimed  that  a 
more  uniform  temperature  was  secured  throughout  all  parts  of  the 
transformer.  It  is  stated  that  no  appreciable  eddy  loss  occurred 
in  the  ribs,  and  that  the  efficiency  of  the  5,5-kw  transformer 
was  about  94,4  per  cent. 

OlL-lMMERSED    TRANSFORMERS 

The  natural  circulation  of  air  affords  insufficient  means  of 
dissipating  the  heat  from  other  than  very  small  transformers, 
and  the  simplest  alternative  consists  in  immersing  the  trans- 
former in  a  tank  of  oil.  If  the  case  is  filled  with  oil  and  if 
suitable  attention  is  given  to  providing  for  a  free  natural 
circulation  of  oil  through  all  portions  of  the  transformer,  then 
the  ultimate  temperature  rise  of  an  oil-immersed  transformer 
will  be  proportional  to  the  watts  total  loss  in  the  active 
material  of  the  transformer  per  square  decimeter  of  external 
radiating  surface  of  the  case.  Oil-immersed  transformers 
were  employed  in  England  at  an  early  date,  but  soon  came 
into  disrepute  owing,  in  my  opinion,  to  a  failure  to  understand 
the  requirements  of  a  design  of  this  kind  and  to  the  use  of 
poor  grades  of  oil.  Suitable  transformer  oil  is  expensive,  but 
the  use  of  the  best  qualities  should  be  rigorously  insisted  upon, 
and,  furthermore,  the  greatest  of  care  should  be  exercised  in 

i2 


116    THE   DESIGN   OF   STATIC   TRANSFORMERS 

keeping  the  oil  clean,  and  free  from  impurities  or  moisture. 
Many  insulating  materials  which  can  be  employed  with  great 
advantage  in  air-immersed  transformers  must  not  be  used  in 
oil-immersed  transformers,  as  not  only  will  the  oil  destroy 
their  good  properties,  but  the  presence  of  these  insulating 
materials  will  destroy  the  good  properties  of  the  oil.  That 


16 


4 


JO 


20 


JO 


40 


SO 


/fated  Output 


n 


FIG.  73.  —  Curve  showing  the  time  taken  for  transformers  of  various  outputs  to 
reach  final  temperature  at  full  load. 


there  can  still  exist  prejudices  against  the  oil-immersed  type 
of  transformer  is  very  remarkable,  and  such  a  state  of  affairs 
is  not  likely  to  long  continue.  Some  ten  years  ago  these 
same  strong  prejudices  existed  in  certain  large  electrical  manu- 
facturing firms  in  Germany,  but  they  have  long  since  been 
overcome,  and  the  appropriateness  of  the  oil-immersed  type 
for  a  wide  range  of  work  is  now  almost  universally  admitted. 


THE    HEATING   OF   TRANSFORMERS 


117 


In  some  investigations  of  transformer  troubles  in  Germany  I 
once  found  an  instance  where  the  oil  was  kept  in  wooden  barrels 
in  the  open  air,  and  in  rainy  weather  pools  of  water  collected  on 
the  heads  of  the  barrels  and  gradually  worked  through  into 
the  oil.  Under  any  such  conditions,  of  course,  the  use  of 
oil  is  fatal,  but  with  reasonable  intelligence,  great  advantages, 
chiefly  as  regards  cooling,  attend  the  use  of  oil  in  transformers 

Centigrade 
60°,        i 


50 


40° 


30 


Af  \rcn  cere 


10 


O        I       23       4       5       6       78       9      IO      n      12     15      14     15     16 

Houro 

FIG.  74. — Heating  curves  of  7,5-kw  Felton-Guillaume-Lahmeyer  transformer. 

The  curve  in  Fig.  73  gives  a  rough  idea  of  the  time  which 
will  elapse  for  a  50-cycle  oil-immersed  transformer  of  repre- 
sentative design  to  reach  its  ultimate  temperature  when 
operated  at  its  rated  load.  Great  variations  exist,  however, 
with  variations  in  the  proportions  and  construction  of  the 
transformer.  Very  large  transformers  require  many  hours  to 
attain  their  ultimate  temperature.  Thus  the  temperature  of 
an  oil-immersed  transformer  of  200-kw.  capacity  may  continue 


118    THE   DESIGN   OF   STATIC   TEANSFOEMEES 

to  rise  for  well  on  toward  twenty-four  hours.  In  Vol.  38  of 
the  Journal  of  the  Institution  of  Electrical  Engineers,  Prof. 
Epstein  publishes  the  curves  of  temperature  rise  reproduced 
in  Figs.  74  and  76,  and  relating  to  transformers  manufactured 
by  the  Felton-Guillaume-Lahineyer  Company.  The  curves 


FIG.  75. — 40  000-volt  oil-immersed  transformer. 

in  Fig.  74  relate  to  a  7,5-kw  transformer,  and  it  will  he  seen 
that  even  at  the  end  of  sixteen  hours  the  curves  of  temperature 
rise  of  the  core  and  the  windings  have  only  just  become  flat. 
The  curves  of  Fig.  76  relate  to  the  temperature  rise  of  the 
40  000-volt  oil-immersed  transformer  illustrated  in  Fig.  75. 
Prof.  Epstein  stated  that  he  had  found  that  "  in  all  his  firm's 
transformers  of  the  same  design,  from  3  up  to  100  kw,  the 


THE   HEATING  OF   TBAN8FOBMEBS 


119 


temperature  became  stationary  after  a  run  of  about  sixteen 
hours,  and  the  temperature  rise  after  a  six-hour  run  was,  for 
all  of  them,  some  80  per  cent,  of  its  final  value  for  the  copper 
and  66  per  cent,  for  the  iron."  As  regards  the  oil  transformer 
illustrated  in  Fig.  75,  and  to  which  the  curves  of  Fig.  76 
apply,  Prof.  Epstein  stated  :  "  The  lower  parts  do  not  heat  at 
all  at  the  beginning  of  the  test.  The  lower  the  thermometer 
is  placed  the  greater  the  difference  between  the  temperature 


" 


•r 


4- 

f- 

I 


10 


FIG.  76. — Heating  curves  of  oil  transformer.     (See  Fig.  77,  for  key  to  positions 
of  thermometers  for  curves  A,  B,  C,  and  D.) 

rise  obtained  after  a  few  hours'  run  and  the  stationary  value." 
The  diagram  in  Fig.  77  indicates  the  positions  of  the  thermo- 
meters corresponding  to  the  four  curves  in  Fig.  76.  Prof. 
Epstein  explained  the  singular  shape  of  the  curves  of  Fig.  76 
as  follows : — 

"As  the  transformer  becomes  heated,  the  warmed  oil  rises 
to  the  surface  and  consequently  the  upper  thermometer  Z) 
will  indicate  the  rise  in  temperature  first,  while  the  lower  ones 
will  not  be  affected  at  the  beginning  of  the  test,  as  there  is  no 


120    THE   DESIGN   OF   STATIC   TKANSFOKMERS 


convection  of  heat  in  a  horizontal  direction.  It  takes  prac- 
tically about  five  hours  before  the  volume  of  oil  at  G  is  heated 
up.  Immediately  after  this  stage  is  reached,  heated  oil  begins 
to  fill  up  the  space  H,  which  process  takes  another  three 
hours,  and  during  this  time  the  rate  of  rise  of  temperature 
proceeds  more  rapidly,  owing  to  the  narrower  space.  As  I  have 
already  pointed  out,  the  question  of  the  rate  of  temperature 
rise  has  nothing  to  do  with  the  size  of  the  apparatus — it  is 
merely  a  question  of  the  ratio  of  two 

•    ^\ 

effects,  viz.,  the  ratio  of  the  cooling- 
surface  to  the  heat  capacity  of  the 
whole  volume.  The  case  of  the  oil- 
transformer  experiment  is  somewhat 
complicated  by  the  motion  of  the 
oil." 

Prior  to  Prof.  Epstein's  explanation 
of  the  curves  of  Fig.  76  (which 
occurred  in  his  reply  to  the  discus- 
sion on  his  paper),  Mr.  J.  S.  Peck  had 
offered  the  following  comments  : — 

"  I  have  made  a  large  number  of 
tests  of  oil  transformers,  but  I  have 
never  before  seen  an  accurate  curve 
which  had  a  hump  in  it  at  the  end  of 


FIG.  77. — Diagram  show- 
ing positions  of  ther- 
mometers for  the  heat- 
ing curves  shown  in 
Fig.  76. 


four  hours.  The  temperature  curve  should  be  a  perfectly 
smooth  one.  It  is  well  known  that  wide  differences  in  tem- 
perature are  obtained  at  different  oil  levels,  as  shown  in  the 
curve,  but  it  seems  remarkable  to  me  that  the  oil  at  the  bottom 
of  the  case  should  remain  cold  for  so  long  a  time." 

The  temperature  rise  of  a  transformer  when  arranged  in  a 
case  containing  air  will  be  very  much  greater  than  the  tem- 
perature rise  of  the  same  transformer  when  contained  in  the 
same  case  filled  with  oil.  Instances  of  this  for  two  trans- 
formers of  5  kva  and  50  kva  rated  capacity  respectively  are 
given  in  the  curves  in  Figs.  78  and  79. 


THE   HEATING   OF   TRANSFORMERS 


121 


FIG. 


78. — Heating  curves  for  5-kva  transformer  in  air  and  oil.     Curve  A  in  case 
without  oil  ;  Curve  B  in  case  with  oil. 


7~ime  in  Mours  on  fu/1  load 


A   -  Jn  Ar 

"         R     -    T     XX  / 

13          ^/7    C/// 

FIG.  79. — Heating  curves  for  50-kva  transformer  in  air  and  in  oil. 


122     THE   DESIGN   OF    STATIC   TKANSFOBMEKS 


Curre,    A  =  f7naf  Temperature  f?/se  /n  /?/r 


FIG.  80.  —  Curves  showing  temperature  rise  of  transformers  in  air  and  in  oil. 

Iii  Fig.  80  are  given  curves  showing  the  final  tempera- 
ture rise  in  air,  the  rise  after  eight  hours  in  air  and  the  rise 
in  oil,  for  a  line  of  oil-immersed  transformers  comprising 


THE   HEATING   OF   TKANSFOKMEKS 


123 


ratings  of  from  1  to  50  kva.  The  temperatures  plotted  in 
the  curves  are  those  of  the  windings  as  determined  by 
measuring  the  resistances  before  and  after  the  tests.  In  the 
instances  of  the  20-,  30-,  and  50-kva  transformers,  when  run 
in  air,  the  figures  for  the  ultimate  temperature  rise  (curve  A) 
are  not  hased  on  actual  observations,  but  are  inferred  from 
the  results  of  the  eight-hour  tests  (curve  B),  since  the  ultimate 
temperatures  would  have  been  so  high  as  to  injure  the 
insulation.  The  curves  show  that  the  difference  in  tempera- 
ture for  air  and  oil  operation  is  greater  for  the  large  than  for 


N 


FIG.  81. — Curve  showing  time  for  50-kva  transformer  to  reach  40°  C.  at 
various  loads. 

the  small  transformers.  The  curve  in  Fig.  81,  which  relates 
to  a  50-kva  oil-immersed  transformer,  shows  the  number  of 
hours  during  which  the  transformer  can  carry  various 
loads  without  sustaining  a  temperature  rise  of  more  than 
40°  above  the  temperature  of  the  room.  The  curve  shows 
that  the  transformer  can  carry  double  its  rated  load  for 
nearly  two  hours  without  sustaining  a  temperature  rise  of 
more  than  40°  if,  at  the  commencement  of  that  time,  its  tem- 
perature is  that  of  the  room  in  which  it  is  installed.  The 
standard  practice  of  most  transformer  manufacturers  is  to 
guarantee  that  at  rated  load  the  temperature  rise  at  the  end  of 


124     THE   DESIGN   OF    STATIC   TBANSFOKMEKS 

eight  hours,  as  determined  in  the  hottest  part  of  the  oil,  shall 
not  be  more  than  some  40°  to  45°  above  the  temperature  of 
the  room.  It  would  be  much  better  to  stipulate  that  the 
ultimate  temperature  rise  as  thus  determined  should  not  be 
more  than  50°  (or  preferably  45°)  above  room  temperature. 

The  Engineering  Standards  Committee's  Eeport  No.  36  of 
August,  1907,  contains  (on  pp.  13  and  14)  the  following  clauses 
dealing  with  the  temperature  rise  of  transformers  : — 

"  (vn.)  For  alternating- current  transformers,  whether  oil-cooled  or 
otherwise,  in  which  cotton,  paper  and  its  preparations,  linen,  micanite, 
or  similar  insulating  materials  are  employed,  80°  C.  shall  be  the  highest 
mean  temperature  permissible. 

"  (viu.)  They  shall  be  run  on  load  for  a  period  sufficiently  long  to 
enable  the  transformer  to  attain  such  a  temperature  that  the  increase  of 
temperature  does  not  exceed  1°  0.  per  hour.  Under  these  conditions  the 
observed  temperature  rise  at  the  hottest  part,  as  determined  in  Clause  (x.), 
shall  not  exceed  50°  C.,  based  on  the  assumption  that  the  air  temperature 
of  the  room  in  which  the  transformer  is  to  be  used  in  actual  service  will 
not  exceed  25°  C. 

"  (ix.)  If  the  air  temperature  of  the  room  in  which  the  transformer  is 
to  be  used  in  actual  service  may  exceed  25°  C.,  then  the  temperature  rise 
specified  above  is  to  be  decreased  by  one  degree  for  each  degree  of 
difference  between  the  room-temperature  possible  and  25°  C. 

"  (x.)  In  the  case  of  air-cooled  transformers  the  temperature  shall  be 
ascertained  by  rise  in  electrical  resistance. 

"  (xi.)  In  the  case  of  oil-cooled  transformers  the  temperature  shall  be 
ascertained  by  rise  in  electrical  resistance,  in  addition  to  which  the 
temperature  at  the  surface  of  the  oil  shall  be  ascertained  by  means  of 
a  thermometer,  and  should  the  temperature  obtained  by  the  two  methods 
differ,  the  lower  figure  shall  be  discarded." 

The  following  clause  in  the  Standardisation  Eules  of  the 
American  Institute  of  Electrical  Engineers  relates  to  the 
permissible  temperature  rise  of  transformers  for  intermittent 
service,  and  consequently  to  most  transformers  supplying 
lighting  loads : — 

"  In  the  case  of  transformers  intended  for  intermittent  service,  or  not 
operating  continuously  at  full  load,  but  continuously  in  circuit,  as  in 
the  ordinary  case  of  lighting  transformers,  the  temperature  elevation 
above  the  surrounding  air  temperature  should  not  exceed  50°  C.  by 
resistance  in  electric  circuits,  and  40°  C.  by  thermometer  in  other  parts 


THE   HEATING   OF    TRANSFOEMEES          125 

after  the  period  corresponding  to  the  term  of  full  load.  In  this  instance 
the  test  load  should  not  be  applied  until  the  transformer  has  been  in 
circuit  for  a  sufficient  time  to  attain  the  temperature-elevation  due  to 
core  loss.  With  transformers  for  commercial  lighting,  the  duration  of 
the  full-load  test  may  be  taken  as  three  hours,  unless  otherwise 
specified." 

If  it  is  definitely  known  that  a  transformer,  while  in  circuit 
continuously,  will  only  be  loaded  for  short  periods  and  that 
these  periods  will  be  followed  by  considerable  intervals  of  no 
load  or  of  only  small  loads,  then  obviously  it  is  not  appropriate 
to  provide  a  transformer  capable  of  dealing  with  the  maximum 
load  for  the  entire  twenty-four  hours.  On  the  contrary,  the 
best  results  will  be  obtained  by  employing  a  transformer  which 
will  perform  the  required  service  without  ever  exceeding  a 
reasonable  temperature-rise,  say  40°.  But  commendable 
efforts  to  provide  the  most  suitable  transformer  should  not 
be  confused  with  the  inclination  of  some  manufacturers  of  basing 
their  designs  on  the  assumption  that  their  transformers  will, 
in  a  very  large  percentage  of  instances,  never  be  called  upon  to 
carry  the  rated  load  for  periods  of  more  than  a  very  few  hours 
each.  These  firms  may  designate  as  of  20  kw  rated  capacity 
a  transformer  which  will  be  decidedly  smaller  than  another 
firm's  standard-rated  transformer  and  consequently  having  a 
very  much  smaller  core-loss,  and  in  the  few  instances  in  which 
there  are  complaints,  these  firms  are  well  able  to  afford  to 
replace  their  misleadingly-rated  transformer  by  a  very  liberal 
transformer.  It  is  not  for  the  manufacturer,  but  for  the 
purchaser  or  his  adviser  to  decide  whether  a  certain  trans- 
former will  suffice  for  some  particular  conditions  of  service. 
When  the  manufacturer  represents  his  transformer  as  being 
of  20  kw  capacity  he  is  undertaking  (unless  it  is  otherwise 
expressly  specified)  that  the  transformer  will  carry  20  kw  con- 
tinuously without  exceeding  a  temperature  rise  of  40°  or  45° 
(according  to  the  stipulation)  above  the  room  temperature.  The 
purchaser  may  analyse  the  conditions  and  satisfy  himself  that 
according  to  the  amount  and  duration  of  the  peak  load,  a 


126    THE   DESIGN   OF   STATIC   TRANSFORMERS 

15-kw  or  even  a  12-kw  transformer  will  suffice  for  his 
particular  purpose,  but  this  is  not  within  the  province  of  the 
manufacturer. 

Thus  I  strongly  condemn  such  advice  as  that  preferred 
by  the  engineer  of  a  well-known  transformer-manufacturing 
company  in  the  following  paragraph  : — 

"Perhaps  the  better  course  for  an  engineer  to  adopt  is  that 
of  leaving  the  matter  of  temperature  limits  to  be  filled  in  by 
the  individual  manufacturers,  who  are  specialists,  and  have  their 
reputation  at  stake  when  tendering.  To  arbitrarily  fix  some 
apparently  low  figure,  when  in  reality  nothing  standard  for 
comparison  exists,  is  to  cause  those  manufacturers  who  declare 
their  maximum  temperature  to  put  up  prices  in  order  to  go 
under  what  to  them  must  appear  a  ridiculous  limit. 

"  For  transformers  working  without  cases  under  climatic  con- 
ditions such  as  those  existing,  for  instance,  in  many  a  London 
sub-station,  the  writer  is  of  opinion  that  better  and  safer 
running  may  result  by  permitting  transformer  coils  to  assume 
a  degree  of  warmth  such  as  to  obviate  any  risk  of  break-down 
that  might  result  from  the  depositing  of  moisture  on  the  surface 
of  the  coils. 

"  The  rise  in  temperature  of  the  iron  core  of  a  transformer 
should,  however,  be  kept  well  under  80°  C.  if  any  appreciable 
mechanical  restraint  is  imposed  upon  it,  as  ageing  may  occur 
if  the  temperature  of  highly  annealed  iron  remains  at  80°  C. 
for  long  periods,  and  at  the  same  time  is  subject  to  mechanical 
stresses. 

"  There  appears  to  be  a  very  considerable  difference  of  opinion 
as  to  what  temperature  may  be  permitted  in  a  transformer.  To 
begin  with,  this  limit  of  temperature  should  depend  upon  the 
class  of  insulation  employed.  With  oil-varnishes,  and  insula- 
tions that  oxidise,  the  limit  is  necessarily  a  low  one,  and 
wherever  oil  is  employed,  the  temperature  should  be  kept  down 
to  the  lowest  possible  limits.  The  writer  has  run  transformers 
of  his  own  design  at  temperatures  as  high  as  150°  C.  for  con- 


THE    HEATING   OF   TRANSFORMERS          127 

siderable  periods  together  without  any  apparent  deterioration, 
and  yet  transformer  experts  in  America  and  Germany  have  found 
that  even  so  low  a  temperature  as  70°  C.  rise  is  detrimental  to 
certain  oil-varnish  insulations.  Mica  and  compound  insula- 
tions with  mica  as  a  basis  are  very  often  capable  of  resisting  far 
higher  temperatures  than  those  specified." 

As  opposed  to  the  above  leaning  toward  permitting  high 
temperatures  I  would  recommend  to  the  reader's  attention  the 
following  leading  article  from  the  Electrical  Revieiv  of  August 
18th,  1905  (Vol.  57,  p.  246).  I  am  of  opinion  that,  nowithstand- 
ing  the  five  years  which  have  elapsed  since  it  was  written,  the 
article  is  exceedingly  appropriate  to  the  present  transformer 
situation. 

"  The  Effect  of  Temperature  on  Insulating  Materials  :  The 
Engineering  Standards  Committee  recently  issued  Report 
No.  22  entitled,  '  Report  011  the  Effect  of  Temperature  on 
Insulating  Materials.'  The  report  consists  of  three  sections. 
The  first  section  comprises  the  investigations  carried  out  by 
Mr.  E.  H.  Rayner,  which,  as  an  institution  paper  (Proceedings, 
Institution  of  Electrical  Engineers,  Vol.  34,  p.  613,  March  9th, 
1905),  has  already  received  consideration  in  the  columns  of  the 
Electrical  Review.  In  the  second  and  the  third  sections  are 
given  the  results  of  tests  of  insulating  materials  employed  in 
the  manufacture  of  dynamo-electric  machinery  at  the  works  of 
Messrs.  Crompton  &  Co.,  Ltd.,  and  of  Messrs.  Siemens  Bros. 
&  Co.,  respectively.  These  last  two  sections  contain  a  mass 
of  useful  results  set  forth  in  a  series  of  carefully-prepared 
tables.  In  spite  of  the  fact  that  statements  as  to  the  conditions 
of  test  are  exceedingly  meagre,  the  results  are  very  interesting. 

"  Pending  the  publication  of  results  of  really  exhaustive 
practical  tests,  made  with  a  full  appreciation  of  the  nature 
and  scope  which  should  obtain  in  such  investigations,  it  is 
believed  that  the  data  published  in  this  report  will  be  widely 
consulted,  and  with  advantage  to  the  industry.  It  is,  however 
remarkable  that  at  so  advanced  a  stage  in  the  development 


128     THE   DESIGN   OF    STATIC   TRANSFORMERS 

of  dynamo-electric  machinery,  there  is  still  so  little  apprecia- 
tion of  the  necessity  for  taking  many  details  into  account,  if 
tests  on  insulating  materials  are  to  be  of  thorough  value. 

"  The  samples  of  insulating  materials  were  exposed  to  various 
temperatures  for  from  nine  to  twelve  months,  and  both  reports 
are  in  agreement  in  recording  that  none  of  the  materials  were 
suitable  for  withstanding  a  temperature  of  125  C.  for  this  length 
of  time.  Even  abestos  and  micanite  suffered  at  this  tempera- 
ture, the  latter  in  consequence  of  the  charring  of  the 
material  with  which  the  component  scales  of  the  mica  were 
cemented  together. 

"This  experience  with  high  temperatures  further  demonstrates 
the  wisdom  of  not  at  present  exceeding  the  customary  tempera- 
ture standards.  If  a  thermometrically-determined  temperature 
increase  of  40°  C.  is  permitted,  this  will  frequently  mean  an 
ultimate  temperature  of  70°  C.  as  thermometrically  determined, 
and  of  fully  100°  C.  as  determined  from  resistance  measurements. 
Still  higher  actual  temperatures  will  occur  at  inaccessible  parts 
of  the  machine,  notably  in  those  portions  of  the  field  coils  most 
remote  from  any  duct  or  surface.  Hence,  permitting  a  thermo- 
metric  rise  of  even  40°  C.  above  the  surrounding  temperature, 
brings  us  nearly  to  the  ultimate  temperature  where  the  tests  of 
Messrs.  Crompton  &  Co.  and  of  Messrs.  Siemens  Bros, 
indicate  that  there  are  few,  if  any,  otherwise- suitable  materials 
which  do  not  deteriorate  considerably  in  a  year  or  so.  It  is  to 
be  hoped  that  progress  in  the  production  of  suitable  insulating 
materials  will  be  stimulated  by  the  report  of  the  Engineering 
Standards  Committee,  as  materials  which  will  permit  of  higher 
temperatures  will  be  of  great  value  to  designers  and  manu- 
facturers. The  present,  however,  is  no  time  for  increasing  the 
standard  temperature  rise.  Even  when  apparently-suitable 
materials  are  on  the  market,  a  few  years  must  elapse  before 
their  suitability  can  be  demonstrated  in  actual  practice. 

"  It  required  several  years  of  actual  service  to  demonstrate 
that  the  insulating  materials  formerly  employed  in  railway 


THE    HEATING   OF    TRANSFOEMEKS  129 

motors  ultimately  pulverised  as  the  result  of  exposure  to  the 
combined  effect  of  vibration  and  high  temperature.  Even  at 
present  there  are  plenty  of  manufacturers  who  are  choosing  their 
insulating  materials  more  with  reference  to  price  per  yard,  per 
pound,  or  per  gallon,  as  the  case  may  be,  than  to  whether  the 
apparatus  in  which  it  will  be  employed  will  be  subject  to  heat, 
moisture,  or  vibration,  or  to  other  deteriorating  influences.  Most 
electrical  manufacturers  are,  however,  desirous  of  employing 
sound  materials  and  of  keeping  within  as  conservative  tempera- 
ture limits  as  the  competitive  struggle  will  permit. 

"  Raising  the  standard  temperature-limit  would  simply  result 
in  a  general  lowering  of  the  price  per  horse-power  or  per 
kilowatt.  Competition  would  keep  the  manufacturer's  profits 
as  low  as  ever,  and  even  the  customer  would  not  benefit,  since 
his  motors  and  dynamos  would  be  subject  to  a  greater  rate  of 
depreciation.  Such  a  result  would  tend  to  bring  discredit  upon 
the  electrical  industry. 

"  The  temperature  limit  should  be  raised  by  small  amounts 
from  year  to  year,  keeping  pace  with  the  gradual  progress  made 
in  the  development  of  improved  insulating  materials.  It  will 
not  suffice  to  produce  one  or  two  insulating  materials  capable  of 
also  withstanding  a  high  temperature,  for  the  requirements  of 
the  manufacturer  of  dynamo-electric  machinery  are  only  met  by 
the  employment  of  many  different  insulating  materials." 1 

1  As  further  bearing  upon  this  important  subject  of  combating  the  tendency 
to  permit  higher  temperatures,  I  propose  to  quote  Mr.  E.  G.  Reed,  who,  in  an 
important  paper  on  Transformers,  read  at  the  32nd  Annual  Convention  of 
the  National  Electric  Light  Association,  in  June,  1909,  puts  the  case  as 
follows  : — 

"Transformers  operating  at  a  temperature  of  100  degrees  Centigrade  will 
probably  soon  fail,  and  assuming  an  average  temperature  of  the  air  of 
25  degrees  Centigrade,  this  limits  the  maximum  permissible  temperature  rise  of 
the  transformer  to  less  than  75  degrees  Centigrade.  Allowing  a  margin  of,  say, 
10  to  15  degrees  Centigrade,  gives  a  safe  operating  temperature-rise  of  from 
60  to  65  degrees  Centigrade.  This  refers  to  the  temperature  rise  of  the 
windings  and  not  to  that  of  the  surrounding  oil,  which  obviously  must  be 
cooler.  In  good  commercial  transformers,  depending  on  the  size  and  on  the 
cooling  efficiency  of  the  oil-ducts  through  the  windings,  the  temperature  of  the 
windings  is  from  5  to  15  degrees  above  that  of  the  hot  oil  in  the  upper  part  of 

S.T.  K 


180     THE    DESIGN   OF    STATIC   TRANSFOKMEKS 
KELATION  BETWEEN  TEMPER ATUEE  RISE  AND  OUTPUT 

Although  it  is  practicable  to  increase  the  rating  of  a  trans- 
former, provided  a  higher  temperature  rise  is  allowable,  and 
although  this  is  often  done  in  practice,  it  is  not  to  be  recom- 
mended. Not  only  is  the  regulation  rendered  worse,  but  the 
insulation  is  liable  to  deteriorate  if  subjected  to  high  tempera- 
ture. The  rating  of  a  transformer  designed  for  a  temperature 
rise  of  40°  C.  may  usually  be  increased  some  15  per  cent,  for  a 
temperature  rise  of  50°  C.,  and  some  40  per  cent,  for  a  60°  C. 
rise.  The  price  of  a  transformer  designed  for  a  higher  rating 
and  temperature  rise,  but  with  the  same  amount  of  material, 
would  be  substantially  the  same  as  for  the  lower  rating  and 
temperature  rise.  A  transformer  of  a  given  rating  and  with 
high  temperature  rise  may,  however,  be  built  cheaper  than  one 
of  equal  rating,  but  with  normal  temperature  rise.  A  com- 
parison of  two  transformers  built  by  a  certain  large  manufactur- 
ing firm  is  given  in  Table  13,  and  bears  on  this  point. 


TABLE  13. — COMPARISONS  OF  COST  OF  HIGH  AND  Low  TEMPERATURE- 
RISE  TRANSFORMERS. 


High  temp.  rise. 

Low  temp.  rise. 

Output  (in  kw.)        ..... 
Periodicity  (in  cycles  per  sec.)          .       •• 

7,5 
60 

7,5 
60 

Total  loss  (watts)      .         .         . 

245 

250 

Efficiency  (per  cent.)         .... 

96,9 

96,8 

Temperature  rise  (degrees  Centigrade)     . 
Cost  of  active  material  (in  shillings) 

60° 
390 

45° 
470 

the  case.  The  temperature  guarantee  of  standard  distributing  transformers  is 
50  degrees  Centigrade  rise  of  the  windings  after  continuous  operation  at  normal 
load.  If  this  guarantee  were  based  on  oil  temperatures,  rather  than  on  that  of 
the  windings,  a  guarantee  of  approximately  40  degrees  Centigrade  could  be 
made  instead  of  50  degrees  Centigrade.  In  determining  the  permissible  load  at 
which  commercial  transformers  can  be  operated  for  a  given  time,  and  the 
permissible  time  for  a  given  load,  this  maximum  operating  temperature  must 
hot  be  exceeded." 


THE   HEATING   OF    TRANSFORMERS  131 

ESTIMATION  OF  THE  TEMPERATURE  RISE. 

In  estimating  the  temperature  rise  in  oil  transformers,  a 
leading  factor  relates  to  the  capacity  of  the  case  for  emitting 
heat  from  its  outer  surface.  The  temperature  rise  may  be 
estimated  from  the  basis  of  the  loss  per  unit  of  external  radiating 
surface  of  the  transformer  case.  Thus  we  require  to  know  the 
rate  of  generation  of  heat  in  the  transformer  per  square 
decimeter  of  external  radiating  surface  of  the  case.  This  is 
equal  to  the  total  of  the  watts  lost  in  the  transformer  divided 
by  the  total  external  radiating  surface  of  the  case.  The 
quotient  bears  a  well- denned  relation  to  the  temperature  rise, 
the  two  quantities  being  proportional. 

The  specific  temperature  rise  is  denned  as  the  temperature 
rise  in  degrees  centigrade  per  watt  per  square  decimeter  of 
external  surface  of  the  case,  and  since  this  quantity  has  a  fairly 
uniform  value,  the  permissible  value  of  the  watts  per  square 
decimeter  as  denned  above  depends  on  the  specified  tempera- 
ture. For  example,  if  a  certain  transformer  has  a 
temperature  rise  of  40°  C.,  and  if  the  losses  amount  to  4  watts 
per  sq  dm  of  external  surface  of  the  case,  the  specific 

temperature  rise  is  equal  to  (  —  =:)  10°  per  watt  per  sq  dm. 

The  following  data  afford  a  rough  basis  for  estimating  the 
temperature  rise  of  oil-immersed  transformers  : — 

A.  With  iron  cases  with  a    smooth    external  surface,    the 
specific  temperature  rise  may  be  taken  as  10°  per  watt  per 
sq  dm  of  external  surface  of  the  case.     Hence,  for   40°    C. 
ultimate   rise    the   internal    losses    may   amount   to  4  watts 
per  sq  dm  of  external  surface. 

B.  With   ribbed  iron    cases,    where   the    radiating    surface 
obtained  by  the  addition  of  the  ribs  amounts  to  at  least  twice 
the  surface  of  the  case  without  the  ribs,  the  radiating  capacity 
may  be  taken  as  increased  by  50  per  cent.,  and  the  temperature 
rise  will  be  some   6°  to  7°  per  watt  per  sq  dm  of  external 

K2 


132     THE   DESIGN   OF    STATIC   TRANSFORMERS 

surface  of  the  case,  not  including  in  this  expression  the 
increased  surface  provided  by  the  ribs. 

The  temperature  rise  is  in  all  cases  estimated  from  the  total 
watts  loss  in  the  transformer  divided  by  the  total  external 
smooth  surface  of  the  case,  this  surface  of  reference  being  the 
cylindrical  surface  at  the  root  of  the  ribs.  The  temperature 
rise  is  taken  as  the  rise  above  the  temperature  of  the  surround- 
ing air  when  indicated  by  a  thermometer  placed  in  the  oil  at 
the  hottest  part,  which  is  usually  near  the  top  of  the  core  of 
the  transformer. 

These  constants  (i.e.,  for  cases  A  and  B)  relate  to  the 
ultimate  temperature  rise  for  continuous  running  when  the 
transformer  has  attained  a  steady  temperature.  The  time 
taken  for  medium-sized  oil-immersed  transformers  to  attain  a 
steady  temperature  is  generally  at  least  10  hours.  After  six 
hours  the  temperature-rise  in  such  transformers  is  often 
of  the  order  of  seven-tenths  of  the  ultimate  rise.  Hence,  if 
transformers  are  required  to  be  designed  for  40°  rise  after  six 
hours'  run  (and  not  40°  ultimate  temperature  rise),  the  value  of 
the  watts  per  sq  dm  may  be  some  1,4  times  the  values  given 
above.  Thus,  for  guarantees  of  40°  rise  after  six  hours, 
smooth-case  transformers  may  be  proportioned  for  some  5  to  6 
watts  per  sq  dm.  But  it  is  best  to  keep  the  value  down,  since 
estimates  of  temperature  rise  are,  at  the  best,  only  very  rough. 
An  air-cooled  transformer  has  generally  only  some  two-thirds 
of  the  heat-emitting  capacity  of  the  same  transformer  in  the 
same  case,  but  immersed  in  oil. 

The  extent  to  which  the  heat-emitting  capacity  is  increased 
by  the  addition  of  ribs  on  the  exterior  of  the  case  is  fairly  repre- 
sented by  the  statement  B  above.  The  total  external  cooling 
surface  may  be  increased  to  far  more  than  twice  the  smooth 
surface  of  the  case  by  the  addition  of  very  deep  and  numerous 
ribs.  The  cooling  capacity  is  not,  however,  increased  nearly  in 
proportion,  for  the  ends  of  the  ribs  are  so  removed  from  the 
surface  of  the  case  as  to  be  much  less  effective.  Consequently 


THE    HEATING   OF    TRANSFORMEKS 


133 


little  gain  will  be  made  by  employing  ribs  of  such  dimensions  as 
increase  the  surface  by  much  more  than  two  or  three  times,  and 
for  such  proportions  the  above  data  will  hold  fairly  true.  In  the 
early  days  of  oil-immersed  transformers  it  was  sometimes  the 
practice  to  provide  ribs  both  inside  and  outside  of  the  case,  but 
the  ribs  inside  are  of  relatively  little  use  for  the  reason  that  the 
heat  is  transferred  from  the  oil  to  the  case  much  more  readily 
than  it  can  be  transferred  from  the  case  to  the  surrounding  air. 
The  heating  data  set  forth  in  the  preceding  paragraphs  is 
presented  in  orderly  form  in  Table  14. 

TABLE  14. — CONSTANTS  FOR  THE  ESTIMATION  OF  THE  HEATING 
OF  TRANSFORMERS. 


Air  Immersed. 

Oil  Immersed. 

Smooth. 

Ribbed. 

Smooth. 

Ribbed. 

Ultimate  temperature  rise  in 

degrees  per  watt  per  sq  dm  . 

15°  0. 

12°  0. 

10°  0. 

6,7°  C. 

Watts  per  sq  dm  per  1°  rise     . 

0,067 

0,084 

0,10 

0,15 

Watts  per  sq  dm  for  40°  ulti- 

mate rise      .... 

2,7 

3,3 

4 

6 

Watts  per  'sq  dm  for  40°  rise 

after  6  hours 

3,8 

4,7 

5,7 

8,5 

METHODS  OF  MEASURING  TEMPERATURES 

The  guarantees  given  by  manufacturers  for  the  temperature 
rise  of  their  transformers  must  be  taken  with  caution  unless 
the  method  of  determining  the  temperature  rise  is  clearly 
stated.  That  considerable  precision  of  statement  is  necessary 
when  framing  temperature  guarantees  will  appear  from  the 
following  considerations : — 

In  the  first  case  there  may  often  be  a  difference  of  tem- 
perature of  some  6°  to  12°  or  more,  between  measurements  of 
the  resistances  of  the  windings  and  measurements  by  ther- 
mometers placed  in  the  hottest  accessible  part  of  the  oil. 
This  difference  is,  of  course,  readily  accounted  for.  Also 
the  ratio  of  the  maximum  temperature  of  the  oil  in  an 


134     THE   DESIGN   OF    STATIC   TRANSFORMERS 

oil-cooled  transformer  to  the  average  external  temperature  of 
the  case  may  be  very  high,  especially  in  some  designs  employ- 
ing large  amounts  of  oil  for  cooling  purposes.  The  ratio 
varies  in  commercial  transformers  from  1,4  when  the  circulation 
is  good,  up  to  2,0  on  transformers  with  bad  circulation.  The 
ideal  figure  for  this  ratio  would  obviously  be  unity.  A 
difference  of  temperature  will  be  observed  between  readings  of 
thermometers  placed  on  the  outside  of  the  case  and  of  ther- 
mometers placed  in  a  corresponding  position  inside  the  case. 

The  temperature  rise  is  generally  specified  as  the  average 
from  the  primary  and  secondary  windings  when  taken  by  the 
resistance  method,  and  as  the  maximum  thermometricalty- 
determined  temperature  of  the  oil.  This  is  generally  found  to 
be  at  a  point  just  above  the  top  of  the  core. 

Contrary  to  the  generally-accepted  view  that  the  results 
obtained  by  the  resistance  method  of  measurement  of  the 
temperature  of  the  windings  are  higher  than  those  obtained 
by  thermometric  measurements,  the  reverse  may  be  the  case 
in  transformers  employing  large  amounts  of  oil.  There  is 
usually  a  very  considerable  difference  in  temperature  between 
the  oil  at  the  top  and  at  the  bottom  of  the  tank  in  oil- 
immersed  transformers  of  very  large  capacities,  and  this 
difference  depends  upon  the  size  and  shape  of  the  actual 
transformer  in  relation  to  the  size  and  shape  of  the  case 
within  which  it  is  placed.  When  the  temperature-rise  of  the 
coils  is  measured  by  thermometers,  the  measurements  relate  to 
the  hottest  part  of  the  windings,  since  that  part  of  the 
windings  which  is  nearest  the  surface  of  the  oil  is  usually  the 
part  in  which  the  thermometers  are  placed.  It  may  conse- 
quently be  safety  assumed  that  if  the  temperature  of  this  part 
of  the  windings  is  within  the  guaranteed  limits,  the  tempera- 
tures of  all  other  parts  will  also  be  within  these  limits.  In 
large  oil-cooled  transformers,  more  especially  when  they  are 
placed  in  very  deep  cases,  it  is  often  found  that  the  tempera- 
ture-rise of  the  windings,  when  calculated  by  the  observed 


THE    HEATING   OF    TKANSFOKMERS  185 

increase  of  resistance,  is  less  than  that  obtained  by  thermo- 
metric  measurements.  This  is  because  the  average  tempera- 
ture of  the  windings  is  less  than  that  of  their  upper  portion. 
Thus  thermometric  measurements  may  sometimes  afford  a 
more  correct  indication  of  the  maximum  temperature  in  any 
part  of  the  winding  than  measurements  based  on  the  increase 
of  resistance  of  the  windings.  However,  the  small  depth  of 
oil  in  small-sized  oil-immersed  transformers  is  rarely  sufficient 
to  occasion  this  result,  and  in  small  sizes  the  resistance  method 
will  usually  give  a  more  correct  indication  of  the  maximum 
temperature.  An  objection  to  the  resistance  method  of 
determining  the  temperature  arises  in  the  case  of  transformers 
where  the  windings  are  divided  into  sections  which  are  con- 
nected in  series.  In  such  a  case  the  temperature  calculated  by 
resistance  measurements  is  the  mean  temperature  of  all  the  coils, 
and  therefore  does  not  afford  reliable  indication  as  regards  the 
temperatures  of  individual  coils,  some  of  which  may  be  operating 
at  temperatures  much  higher  than  the  mean  temperature. 

Comparison  of  various  types  of  transformers  as  regards  heating. 
— While  either  the  shell  or  the  core  type  of  transformer  may 
be  so  designed  as  to  conform  to  any  reasonable  specification 
with  respect  to  temperature  rise,  I  nevertheless  consider  that 
the  shell  type  is  distinctly  inferior  to  the  core  type  as  regards 
adaptability  to  oil  immersion.  In  either  type,  ducts  through 
which  the  oil  shall  circulate  may  be  readily  provided,  but 
there  would  appear  to  be  no  such  natural  arrangement  possible 
for  the  shell  type  as  that  of  which  our  20-kva  transformers  of 
Figs.  49,  50,  51,  53,  54  and  55,  are  typical  examples.  Both 
coils  and  core  are  well  bathed  with  the  circulating  oil.  In  the 
shell  type  the  coils  are  less  readily  cooled  than  the  core  unless 
valuable  space  be  sacrificed  in  the  winding  window.  The 
circular-shell  type  represented  diagrammatically  in  Figs.  3 
and  4  is  still  more  greatly  inferior  as  regards  the  difficulty  of 
cooling  the  copper,  and  it  is  significant  that  it  is  the  exploiters 
of  the  circular-shell  type  who  have  displayed  the  greatest 


136     THE    DESIGN   OF    STATIC    TKANSFORMERS 

concern  and  eagerness  that  the  permissible  temperature  rise 
should  be  increased  above  that  at  present  generally  accepted. 

But  in  very  small  transformers  (i.e.,  transformers  from,  say, 
2  k\v  rated  capacity  downwards),  the  question  of  heating  does 
not  control  the  design,  for  if  the  transformer  is  designed  for 
good  regulation  and  low  core  loss,  it  will  also  be  a  correct 
design  as  regards  heating.  Consequently  the  course  of  events 
as  regards  oil-immersed  transformers  will,  in  virtue  of  inevitable 
evolutionary  processes,  in  all  probability  be  in  the  direction  of 
the  general  use  of  the  core  type  for  large  sizes  and  of  various 
types  for  very  small  sizes.  In  very  small  sizes,  particularly 
transformers  for  1  kw  output  and  less,  the  labour  cost  and  the 
establishment  charges  constitute  a  very  large  component,  and 
it  is  less  imperative  to  select  a  type  requiring  a  minimum  of 
material. 

Quantity  of  oil  used  in  transformers. — In  the  early  days 
of  oil-immersed  transformers,  the  idea  was  to  immerse  the 
transformer  in  oil,  in  a  case  of  just  sufficient  size  to  contain 
the  transformer.  A  transformer  designed  on  this  plan  to 
comply  with  customary  heating  specifications  will  run  at 
needlessly-low  current  densities,  and,  except  as  regards  pres- 
sure regulation,  the  rating  may  be  considerably  increased 
if  by  any  means  the  temperature  rise  may  be  maintained 
within  specified  limits.  By  placing  the  transformer  in  a  case 
with  sufficient  radiating  surface,  the  temperature  rise  may  be 
kept  within  the  desired  limits  without  increasing  the  size  of 
the  transformer  itself,  i.e.,  without  increasing  the  amount  of 
material  in  the  windings  and  core. 

It  is  still  the  practice  of  some  manufacturing  firms  to  provide 
cases  of  only  just  sufficient  size  to  contain  the  transformers  and 
to  fill  in  the  intervening  space  with  oil.  For  small  tranformers 
on«  may,  by  this  plan,  be  able  to  obtain  sufficient  radiating 
surface,  but  for  large  ratings  it  is  insufficient.  Such  practice 
leads  either  to  a  great  weight  of  active  material  per  kw  of 
output,  if  the  temperature  rise  is  not  to  be  excessive,  or  to  an 


THE   HEATING   OF   TRANSFORMED 


137 


excessive  temperature  rise  if  the  transformer  is  given  the  rating 
of  which,  in  a  larger  case,  it  would  be  capable.     There  is  a 


7  ^  //O  J° 

\   \  I  1  |  *  *  § 


remarkable  discrepancy  between  the  quantity  of  oil  used  by 
various  manufacturers.     In  Fig.  82  is  given,  for  the  product 


138     THE    DESIGN   OF    STATIC    TKANSFOKMERS 

of  several  makers,  curves  in  which  the  quantity  of  oil  employed 
is  plotted  as  a  function  of  the  rated  output.  Since  these  curves 
relate  to  the  product  of  different  makers,  they  should  not  be 
taken  as  representing  progress  in  transformer  design  during 
the  past  few  years,  but  rather  as  representative  of  widely- 
employed  proportions.  The  values  given  by  the  curve  apply- 
ing to  my  own  designs  appear  very  high  as  compared  with  the 
values  corresponding  to  the  other  curves.  This  is  accounted 
for  by  several  reasons.  The  transformers  corresponding  to 
this  curve  are  designed  with  modern  alloyed  steel  laminations 
which  render  the  transformers  comparatively  small  as  com- 
pared with  the  older  makes  to  which  the  other  curves  in 
Fig.  82  refer.  The  cases  and  quantities  of  oil  for  these 
transformers  are  so  proportioned  as  to  ensure  an  ultimate 
temperature  rise  of  not  more  than  40°  C.  above  the  surrounding 
air. 

With  transformers  having  as  small  quantities  of  oil  as  corre- 
spond to  some  of  the  curves  in  Fig.  82,  it  is  doubtful  whether 
the  temperature  rise  would  not  be  excessive  if  the  transformers 
were  run  at  full  load  for  many  hours  or  until  the  ultimate 
temperature  corresponding  to  continuous  running  is  attained. 
Under  practical  conditions,  a  transformer  is,  after  shipment, 
rarely  operated  at  full  load  for  other  than  short  periods,  and 
thus  there  is  rarely  occasion  to  observe  whether  the  temperature 
rise  conforms  to  the  specified  limit,  and  there  is  thus  a  tempta- 
tion to  take  unscrupulous  advantage  of  this  circumstance. 

The  transformer  cases  proportioned  to  conform  to  my  curve 
in  Fig.  82  are  designed  on  the  principle  that  the  temperature 
rise  may  be  kept  down  to  practically  any  value  which  could 
reasonably  be  specified  by  providing  a  case  of  sufficient  surface 
to  dissipate  the  heat  generated  by  the  losses.  In  other  words 
the  temperature  rise  is,  for  a  given  type,  fairly  proportional  to 
the  watts  per  square  decimeter  of  external  surface  of  the  case. 
Hence,  a  transformer  may  be  designed  to  be  of  small  dimen- 
sions, weight  and  cost  (for  copper  and  core),  provided  that  it 


THE   HEATING   OF   TRANSFORMERS          139 


is  put  into  a  sufficiently  large  case  with  free  circulation  of  the 
oil.     Any  sacrifice  in  efficiency  will  be  but  slight,  since  while 


60 


nse 


6     7     Q     9    /O    //    /Z  /3 

7/7 


FIG.  83.  —  Temperature  curves  for  10-kva  single-phase  oil-cooled  transformer  in 
small  and  large  cases. 

the  heat-loss  per  kilogram  of  active  material  is  high,  the  total 
weight  of  active  material  is  low. 


140     THE   DESIGN   OF    STATIC   TRANSFORMERS 


This  principle  should  not,  however,  be  carried  to  extremes, 
since  there  is  a  limit  beyond  which  excessive  local  heating 
occurs  in  parts  of  the  transformer.  For  the  range  of  practical 


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propositions,  such  dimensions  as  would  give  rise  to  this 
occurrence  are,  however,  not  likely  to  be  approached,  and  the 
principle  has  not  yet  been  applied  to  the  full  extent  which  will 
be  attended  with  commercial  advantage. 

As  illustrative  of  the  above  method   of  designing,  there  are 


THE    HEATING    OF   TRANSFORMERS 


141 


given  in  Fig.  83  temperature  curves  for  a  10-kva  50-cycle 
2000 :  210-volt  single-phase  oil-immersed  transformer  which 
was  tested  at  full  load  in  two  different  sizes  of  case.  The 
relative  sizes  of  the  two  cases  are  shown  in  Fig.  84.  The 
heating  data  for  these  two  tests  are  as  follows  :— 


Small  Case. 

Large  Case. 

Gallons  of  oil         

18 

38 

External  radiating  surface  of  case  in  sq  dm 

103 

166 

Watts  per  sq  dm   ....... 

5,3 

3,3 

Ultimate  temperature  rise  (degrees  Centigrade)    . 

70° 

35° 

Specific  temperature  rise    (in  degrees  per  watt 

per  sq  dm)           

13 

11 

From  these  figures  it  is  seen  that  for  this  particular  trans- 
former (or  these  particular  tests)  the  temperature  rise  was 
halved  by  increasing  the  radiating  surface  by  60  per  cent.  The 
specific  temperature  rise  is  13  and  11  respectively,  the  higher 
figure  relating  to  the  higher  temperature.  The  results  must 
be  taken  as  liable  to  quantitative  error,  but  as  strongly  con- 
firming the  correctness  of  the  principle. 

In  the  above  tests  the  temperature  was  thermo metrically 
determined  at  a  point  near  the  top  just  below  the  surface  of 
the  oil.  The  temperature  at  such  a  point  is  usually  the 
maximum  which  occurs  in  an  oil-immersed  transformer. 
Indeed  the  temperature  at  all  points  in  the  oil  above  the  top  of 
the  core  is  usually  quite  uniform.  The  temperature  at  other 
parts  of  the  transformer  usually  varies  greatly  and  is  a 
minimum  at  the  bottom  of  the  case. 

Fig.  85  shows  a  set  of  temperature  curves  for  the  same 
10-kva  single-phase  oil-immersed  transformer,  but  loaded  to  only 
8  kw.  The  positions  of  the  three  thermometers  T.1,  T2  and 
T3,  are  shown  in  Fig.  84.  These  curves  show  clearly  the 
temperature  distribution  and  also  the  rate  at  which  the 
temperature  increases  at  different  parts.  Tl,  at  the  top  of 
the  case,  rises  rapidly  at  first,  and  then  at  a  decreasing  rate 


142     THE    DESIGN    OF    STATIC   TBANSFOEMEKS 

until  the  ultimate  temperature  is  reached.  This  is  the  case 
because  the  oil  rises  to  the  top  after  being  heated  by  the  trans- 
former. T2,  situated  near  the  body  of  the  transformer  which 
is  the  seat  of  the  losses,  presents  a  similar  characteristic 
although  the  value  of  the  temperature  is  not  so  great.  T3,  at 
the  bottom  of  the  case,  presents  a  different  shape  of  heating 


><?2°C 


2      3      <?      5       6       '/      <3       S> 

7/w^    //?  Hours  . 


/O     //      /£     /3     /-f 


C. 


FIG.  85. — Temperature  test  on  a  10-kva  single-phase  transformer,  with  a  load  of 
8  kw.     (For  positions  of  thermometers  Tl5  T2,  T3,  see  Fig.  84.) 

curve.  The  temperature  rises  very  slowly  at  first  for  a  con- 
siderable number  of  hours,  and  then  more  rapidly  as  the  entire 
transformer  becomes  heated  up. 

This  fact  has  been  also  pointed  out  by  Epstein  l  and  some  of 
his  tests  have  already  been  shown  in  Fig.  76  (p.  119).  It  will  be 
observed  that  the  lower  the  thermometer  is  placed  in  the  oil 

1  "  Testing  of  Electric  Machinery  and  of  Materials  for  its  Construction/' 
Jour.  Inst.  Elec.  Engrs.,  Vol.  XXXVIII.,  p.  49. 


THE   HEATING   OF   TRANSFORMERS 


143 


the  greater  the  difference  between  the  temperature  rise 
obtained  after  a  few  hours  run  and  the  stationary  value.  The 
curves  A,  B,  C  and  D  of  Fig.  76  (p.  119)  refer  to  the  tempera- 
tures given  by  thermometers  placed  in  the  positions  shown  in 
Fig.  77  (p.  120). 

The  effect  of  varying  the  depth  of  oil  in  a  transformer  placed 
in  a  given  case  is  illustrated  by  the  data  given  in  Table  15. 
These  data  refer  to  a  100-kva  5000  to  2000-volt  60-cycle 
single-phase  transformer.  The  first  heating  test  was  made 
with  a  depth  of  oil  of  only  7  cm  above  the  transformer  core. 
The  figures  show  that  not  only  is  the  temperature  of  the  trans- 
former considerably  decreased  by  the  extra  depth  of  oil,  but 
that  the  distribution  of  temperature  is  much  more  even 
throughout  the  whole  volume  of  the  oil,  thus  showing  a  better 
circulation. 

TABLE  15. — HEATING  TESTS  ON  A  100-KVA  TRANSFORMER. 


Test  1. 

Test.  2. 

Depth  of  oil  above  core  in  cm    .... 

7 

30 

Oil  radiating  surface  (exclusive  of  bottom  of 

case),  [sq  dm]          .         «                 .        .  .    ••' 

441 

532 

Watts  dissipated          .         .        .        .        « 

1430 

1300 

Watts  per  sq  dm          

3,24 

2,44 

Temperature  at  top  of  punchings  after  24  kr 

40°  C. 

36°  0. 

,,            of  oil  at  surface  (close  to  case) 

40°  C. 

36°  0. 

,,             ,,  case  at  surface  of  oil. 

27°  C.' 

32°  0. 

,,             ,,  case  half-way  down  .    •     . 

23°  C. 

20°  C. 

Height  from  bottom  of  case  at  which  no  furthe 

temperature  rise  was  recorded  after  24  hr 

33  cm 

18  cm 

Temperature  of  primary  by  resistance  measure 

ments      ........ 

62°  C. 

58°  C. 

Temperature      of      secondary     by     resistance 

measurements          

50°  C. 

41°  C. 

Specific  temperature  rise  in  degrees  per  watt 

per  sq  dcm       .*,.... 

12,3 

14,7 

In  considering  the  somewhat  high  specific  temperature  rises 
recorded  in  these  tests,  the  length  of  time  for  which  the  tests 
were  made,  namely,  twenty-four  hours  at  full  load,  must  be 
kept  in  mind. 


144     THE   DESIGN   OF    STATIC   TRANSFORMERS 

Ventilation  Ducts. — It  is  desirable  that  the  temperature 
throughout  the  transformer  should  be  as  uniform  as  possible, 
and  that  there  should  be  no  excessive  local  heating  at  any 
part  of  the  transformer.  In  the  interests  of  achieving  this 
result,  the  windings  and  core  should  be  provided  with  ducts 
or  channels  through  which  the  oil  can  circulate.  In  older 
designs  of  transformers  this  provision  was  not  made,  and  the 
maximum  temperature  attained  was  considerably  in  excess  of 
the  temperature  at  any  accessible  part.  In  a  modern  trans- 
former liberally  provided  with  wide  ventilating  ducts,  there  is 
much  less  liability  to  local  heating,  and  the  ratio  of  the 
maximum  temperature  to  the  highest  accessible  temperature 
does  not  vary  greatly  from  unity. 

In  large  transformers  it  is  absolutely  essential  in  the  interests 
of  maintaining  the  insulation  in  good  condition,  to  provide 
ventilating  ducts  both  in  the  windings  and  the  core.  In  the 
case  of  transformers  of  the  core  type  I  usually  prefer  the 
arrangement  of  the  ventilating  ducts  illustrated  in  Figs.  49, 
50,  51,  53,  54,  and  55.  In  this  construction  the  coil  is 
separated  from  the  core  by  means  of  specially-shaped  distance 
strips  of  suitably-impregnated  wood  or  other  material.  In  this 
manner,  parts  of  the  inside  of  the  coils,  as  well  as  of  the  out- 
side, are  subject  to  the  cooling  effects  of  the  oil.  It  is  most 
desirable  to  avoid  undue  local  heating,  as  this  conduces  to 
ageing  of  the  iron,  and  to  deterioration  of  the  insulation. 


CHAPTER  IX 

TRANSFORMER    CASES    AND    TANKS 

^ 

ANY  one  of  a  variety  of  materials  may  be  employed  in 
the  construction  of  transformer  cases.  The  rated  output 
required  of  the  transformer  and  the  appropriate  mehod  of 
cooling  will  usually  affect  the  choice.  The  principal  materials 
used  are  cast  iron,  galvanised  sheet  iron,  sheet  steel,  and 
boiler  iron.  For  small  sizes  of  transformers  cast  iron  is 
generally  used,  both  for  air-cooled  and  oil-cooled  designs. 
This  is  for  several  reasons.  The  pattern  will,  for  small  sizes, 
not  entail  large  outlay,  and  this  outlay  will  be  spread  over  a 
very  great  number  of  transformers.  Furthermore,  the  cost  of 
iron  castings  is  small.  The  labour  item  in  building  sheet-iron 
cases  for  housing  transformers  of  small  capacity  renders  their 
cost  excessive  when  compared  with  cast-iron  cases  of  similar 
size.  Furthermore,  the  larger  the  case,  the  more  difficult  it  is 
to  cast,  in  view  of  the  small  thickness  of  metal.  In  fact,  owing 
to  this  difficulty  of  obtaining  a  good,  sound,  thin  casting  when 
using  cast  iron,  the  walls  of  the  case  must  be  made  thicker  than 
would  otherwise  be  desirable.  For  this  reason,  and  because 
large  cast-iron  cases  are  much  heavier  than  either  galvanised 
sheet-iron  or  boiler-iron  cases  of  the  same  capacity,  the  cost, 
when  cast  iron  is  used,  is  nearly  or  quite  as  great  for  large 
transformers  as  for  the  sheet-iron  alternative,  especially  since 
the  necessary  patterns  are  more  expensive  the  larger  the  case. 
Sheet-iron  cases  have  also  the  advantage  that  a  much  greater 
height  can  be  employed  with  a  given  thickness  of  metal.  With 
cast  iron  it  is  not  practicable  to  make  any  considerable  increase 
in  surface  for  a  given  thickness  of  cast  iron  and  for  the  same 
floor  space.  In  other  words,  the  height  of  a  cast-iron  case 

S.T.  L 


146     THE   DESIGN   OP   STATIC   TRANSFORMERS 


FIG.  85A. — Elevation  of  ribbed  cast-iron  case. 

cannot  be  greatly  increased  without  also  increasing  the  thick- 
ness of  its  walls,  if  due  regard  is  given  to  the  mechanical  strength 


TKANSFOKMEB  CASES  AND  TANKS 


147 


and  rigidity  of  the  case.     A  cast-iron  case,  with  ribs  to  increase 
the  radiating  surface,  is  shown  in  Figs.  85A  and  85B. 

Another  objection  to  the  employment  of  cast  iron  for  the 
cases  of  oil  transformers  is  the  liability  that  blow-holes,  flaws  and 


cracks  may  occur  in  the  metal.  Since  a  transformer  case  must  be 
absolutely  oil-tight,  any  flaw  renders  the  case  useless.  Thus, 
in  the  event  of  requiring  prompt  delivery  of  some  large  trans- 
former, the  loss  to  the  manufacturer  in  paying  penalties  incident 
to  delay  may  be  considerable  if  the  cast-iron  cases  prove  faulty 
and  have  to  be  rejected.  Nevertheless,  for"  moderately-large 

L2 


148    THE   DESIGN   OF    STATIC   TRANSFORMERS 

transformers  some   firms  employ  deeply-corrugated   cast-iron 
cases.      In   some  instances  the  height   of  the  required  case 
leads  to  difficulties  in  the    manufacture  of  these  corrugated 
castings.    To  overcome  these  difficulties  such  cases  have  some- 
times been  made  in  sections,  which  are  bolted  together  with  a 
lead  lining  between  adjacent  sections.  When  this  plan  is  adopted, 
the  number  of  sections  employed  for  a  given  transformer  may 
be  roughly  obtained  by  dividing  the  losses  of  the  transformer 
by  the  rate  at  which  each  section  is  known  by  experience  to  be 
capable  of  dissipating  heat.     This  plan,  when  applied  to  large 
sizes,  generally  leads  to  a  heavier  and  more  expensive  case  than 
when  corrugated  wrought-iron  plate  is   employed.     Cast  iron 
emits  slightly  more   heat  per  unit  of  surface  than  either  sheet 
iron  or  boiler  iron,  and  this  has  been  put  forward  as  an  argument 
in  favour  of  cast-iron  cases ;  but  the  difference  in  this  respect 
is  too  slight  to  constitute  a  practical  consideration.    Any  flaws 
in  a  cast-iron  case  can  be  autogenous^  welded,  or  they  can  be 
patched  up  with  a  blow-pipe  or  by  other  familiar  workshop 
methods.     Nevertheless,  these  eventualities  may  add  consider- 
ably to    the  cost.     The  sides  of  cast-iron  cases  may  be   con- 
siderably strengthened  when  external  ribs  are  employed ;  and 
consequently  resort  to  ribs  extends  the  usefulness  of  the  cast- 
iron  type  of  case.     This  is  in  addition  to  the  circumstance  that 
by   means   of    the  ribs   a   much  larger   radiating   surface    is 
available  for  heat  emission.     The   minimum  thickness  prac- 
ticable in    cast-iron    cases    (due    regard   being   given  to  the 
danger  of  fracture  during  transit  and  to  the  initial  difficulties 
in  casting)  is  some  8  mm,  the  range  of  thicknesses  used  in 
practice  varying  between  this  figure  and  some  14  mm,  accord- 
ing to  the  size  and  the  weight  of  the  case.     On  the  whole,  the 
disadvantages  associated  with  the   use   of  cast  iron  for  trans- 
former cases,  taken  in  conjunction  with  the  liability  of  fracture 
during  transit,  are  sufficient  to  make  it  generally  preferable  to 
employ  sheet-iron  or  sheet-steel  cases  for  all  but  small-sized 
transformers. 


TBAN8FOBMBB   CASES   AND   TANKS  149 

Sheet-iron  Cases. — For  the  majority  of  transformer  cases,  gal- 
vanised sheet-iron  or  sheet  steel  is  generally  preferable,  owing 
to  the  small  thicknesses  which  suffice  with  such  constructions. 
Another  advantage  of  employing  sheet-iron  or  sheet-steel  for 
transformer  cases,  relates  to  the  lightness  of  such  designs 
as  compared  with  cast-iron  cases,  and  the  ease  with  which  they 
may  be  ribbed,  thus  not  only  providing  a  greater  surface  for 
heat  emission,  but  increasing  the  mechanical  strength  of  the  case. 
The  sheet-iron  is,  however,  generally  used  only  for  the  sides  of  the 
case.  The  bottoms  and  covers  of  the  cases  are  usually  formed 
either  of  cast-iron  or  wrought-iron,  these  being  subsequently 
jointed  to  the  sides  by  some  one  of  several  suitable  methods, 
by  means  of  which  the  joints  may  be  made  oil-tight.  Where 
the  sides  are  constructed  of  sections,  these  sections  may  be 
welded  together,  but  this,  although  sound  practice,  is  expensive. 
Vertical  joints  are  necessary  with  cases  of  corrugated  sheet 
iron,  owing  to  the  fact  that  the  iron  rollers  cannot  corrugate 
iron  of  more  than  a  certain  width.  In  Fig.  86  is  illustrated  a 
satisfactory  method  of  jointing  the  sides  to  the  bottom  of  the 
case.  This  method  consists  in  providing  two  pieces  of  boiler- 
iron  riveted  together  to  form  the  bottom,  in  addition  to  the 
ordinary  cast-iron  base.  These  pieces  of  metal  are  so  un- 
equally dimensioned  that  when  flanged  to  a  certain  height  a 
channel  is  formed  into  which  the  sheet-steel  sides  are  placed. 
Solder  is  then  poured  into  the  channel,  in  order  to  render  the 
joint  oil-tight.  An  alternative  method  of  accomplishing  the 
same  object  consists  in  forming  the  channel  of  two  ribs  cast 
into  the  base  itself.  These  methods  are  both  rather  expensive, 
especially  when  the  corrugations  in  the  sides  are  very  deep, 
since  this  requires  a  large  amount  of  solder  to  fill  in  the  channel. 
The  joint  thus  obtained  is,  however,  quite  oil-tight,  and  the 
method  constitutes  a  reliable  means  of  providing  a  joint  that 
will  continue  to  resist  the  hot  oil  after  the  transformer  has 
been  placed  in  service.  A  cheap  and  frequently-employed 
method  of  jointing  the  base  to  the  sides  consists  in  placing  the 


150     THE   DESIGN   OF    STATIC   TRANSFORMERS 


lower  portion  of  the  sides  into  a  mould,  into  which  molten  iron 
is  poured,  and  which  forms  the  base.  The  method  has  the 
defect  that  blow-holes  may  occur  around  the  joint,  which, 
though  not  sufficiently  pronounced  to  be  detected  at  the  time, 
may,  under  the  continual  influence  of  the  hot  oil,  ultimately 


\ 


FIG.  86. — Method  of  jointing  the  sides  and  bottom  of  a  transformer  case. 

develop  into  leaks.  Ordinary  materials,  such  as  are  used  in 
everyday  workshop  practice  to  fill  in  flaws  in  cast-iron,  are 
useless  for  the  purpose  of  oil  tanks,  since  the  ingredients  of 
which  the}r  are  composed  are  often  readily  dissolved  by  hot 
oil. 

The  mechanical  construction  of  a  sheet-iron  case  requires 
careful  attention,  since  the  thickness  of  the  walls  is  too  slight 
to  permit  that  the  weight  of  the  transformer  shall  be  taken  up 
by  the  sheet  iron  itself.  On  the  contrary,  the  weight  should 


TBANSFORMER   CASES   AND   TANKS  151 

be  borne  entirely  by  bolts  or  massive  lifting-hooks.  If  the  eye- 
bolts  or  lifting-hooks  are  not  suitably  located,  then  considerable, 
injury  may  result  when  lifting,  due  to  buckling  of  the  sides. 
The  sides  may  be  strengthened  by  providing  a  light  angle-iron 
framework,  placed  either  inside  or  outside,  and  it  should  be 
arranged  that  the  weight  of  the  transformer,  when  lifted,  shall 
come  directly  on  this  framework.  In  some  methods  of  handling 
the  weight,  the  eyebolts  are  made  an  integral  part  of  long  bolts 
which  extend  from  the  base  of  the  transformer.  The  entire 
weight  is  thus  carried  by  the  bottom  of  the  case.  Annular 
ditches  may  be  provided  in  the  base  to  catch  any  dripping  or 
leakage  of  the  oil.  The  sheet-iron  walls  vary  in  thickness 
from  1,5  mm  to  4  mm,  according  to  the  size  and  capacity  of 
the  transformer. 


BOILER-IKON  CASES. 

Boiler-iron  cases  are  used  principally  for  large  water-cooled 
and  forced-oil-cooled  transformers  (see  Chapter  X.),  and  in 
special  types  where  great  strength  is  required,  as  in  portable 
transformers.  Their  advantage  lies  principally  in  the  fact  that 
they  are  stronger  and  more  durable  and  are  cheaper  than  sheet- 
iron  cases.  Ordinary  boiler-plates  ranging  between  7  mm  and 
15  mm  in  thickness  are  used,  with  thoroughly  caulked  single- 
riveted  lap-joints,  and  the  construction  provides  a  very  satis- 
factory and  permanent  oil- tight  joint. 

The  maximum  size  for  which  a  transformer  can  be  built 
to  be  self-cooling  is  limited  by  the  amount  of  heat-emitting 
capacity  for  which  the  case  can  be  designed.  Cases  with 
corrugated  sides  are  often  supplied  with  transformers  up  to 
some  750  kva  capacity,  but  beyond  this  size,  the  weight  and 
dimensions  of  the  case  become  so  great  that  some  method, 
other  than  mere  increase  in  size,  must  be  resorted  to  in  order 
to  provide  the  necessary  radiating  surface. 

A  special  type  of  case  has  re.cently  been  developed  by  the 


152     THE   DESIGN   OF    STATIC    TEANSFOKMEKS 

Westinghouse  Co.  with  a  view  to  overcoming  this  difficulty, 
and  it  is  claimed  that  it  is  capable   of  being  designed  for  a 


FIG.  87.— Westinghouse  1000-kva  100000-volt  60-cycle  oil-immersed  self- 
cooled  transformer. 

greater  cooling  capacity  than  has  heretofore  been  attempted 
for  a  self-cooled  transformer.     It  consists  simply  of  a  plain 


TBANSFOKMEK  CASES  AND  TANKS 


153 


boiler-iron  case  to  the  outside  of  which  are  welded  a  number 
of  cooling  tubes.     These  tubes  are  arranged  vertically,  and  are 


FIG.  88. — Johnson  &  Phillips'  600-kva  transformer  for  oil  immersion. 

given  a  90-degree  bend  at  the  top  and  bottom  where  they  enter 
the  case.  The  mechanical  construction  is  very  strong,  and  it 
is  claimed  that  there  is  practically  no  chance  of  ever  springing 


154     THE   DESIGN   OF    STATIC   TRANSFORMEES 

a  leak.  As  the  tubes  are  well  separated  from  one  another, 
and  as  the  air  consequently  circulates  very  freely  among  them, 
the  efficiency  of  the  radiating  surface  is  considerably  higher 
than  for  the  ordinary  corrugated  case.  Self-cooled  oil- 
immersed  transformers  are  very  appropriate  for  sub-stations 
wherever  water  for  cooling  purposes  is  either  not  available  or 
else  expensive,  or  where  it  is  of  special  importance  that  the 
transformers  shall  require  but  little  attendance. 

The  Westinghouse  Electric  and  Manufacturing  Co.  has 
recently  built  twelve  1000-kva  100  000-volt  60-cycle  trans- 
formers of  the  above-described  type  for  the  Southern  Power 
Co.  Fig.  87  is  an  illustration  of  the  design.  Of  the 
twelve  supplied,  three  are  for  outdoor  service,  and  nine  are 
installed  indoors. 

In  Fig.  88  is  shown,  out  of  its  case,  a  three-phase,  self- 
cooled,  oil-immersed,  50-cycle  transformer  recently  designed  by 
the  author  for  Messrs.  Johnson  &  Phillips,  and  of  which  two 
are  now  in  service  at  the  generating  station  of  the  Aston 
Manor  Corporation.  The  transformer  is  for  600  kva  at  a 
primary  pressure  of  6300  volts  and  a  secondary  pressure  of 
356  volts.  The  periodicity  is  50  cycles  per  second.  700 
gallons  of  oil  are  used  in  this  transformer. 


CHAPTER  X 

FOKCED-COOLED    TRANSFORMERS 

WITH  the  progress  of  the  introduction  of  electrical  methods, 
the    capacities    required    of    individual   transformers   rapidly 


FIG.  89. — Diagram  showing  construction  of  an  air-blast  transformer. 

increased,  and  manufacturers  experienced  difficulties  in  the 
matter  of  restricting  the  temperature  rise.  Ultimately  they 
turned  their  attention  to  methods  of  forced  cooling,  and  three 


156     THE    DESIGN    OF    STATIC    TRANSFORMERS 

t}7pes  of  forced-cooled  transformers  came   into   extensive  use« 
These   may  be   designated  Air-Blast    Transformers,   Forced- 


FIG-.  90. — Coils  of  a  shell-type  air-blast  transformer  after  completion  of 
impregnating  process. 

Water-Cooled     Oil.    Transformers     and     Forced-Oil-Cooled 
Transformers. 

Air-Blast  Transformers. — A  typical  design  for  a  shell-type 
air-blast  transformer  is  indicated  in  Fig.  89.     A  view  of  the 


FORCED-COOLED   TRANSFORMERS 


157 


coils  of  an  air-blast  transformer  taken  at  a  certain  stage  of  their 
manufacture,  is  given  in  Fig.  90.  By  regulation  of  the  amount 
of  openings  in  the  case  by  means  of  dampers  provided  for 
the  purpose,  the  relative  amounts  of  air  passing  respectively 
through  the  core-ducts  and  through  the  passages  between  the 
coils,  may  be  adjusted.  Air-blast  transformers  are  nowadays 


<D  <2 


FIG.  91. — Diagrammatic  sketch  of  American  General  Electric  Co.'s  air-blast 

transformers. 

rarely  employed  for  units  of  less  than  300  kw  capacity.  The 
general  external  appearance  of  the  type  to  which  Figs.  89  and 
90  apply  is  shown  in  Fig.  91  relating  to  designs  by  the  General 
Electric  Co.  of  America.  In  Fig.  91,  the  overall  dimensions 
A,  B  and  C  are,  for  transformers  for  primary  pressures  of 
some  12  000  volts  and  secondary  pressures  of  some  1000  to 
2000  volts,  and  for  rated  outputs  of  500  kva  and  1000  kva, 
roughly  as  set  forth  in  Table  16. 


158    THE   DESIGN   QF   STATIC   TRANSFORMERS 


FIG.  92. — 550-kva  50-cycle  air-blast  transformer  by  the  Westinghouse  Co. 


FORCED-COOLED   TRANSFORMERS  159 

TABLE  16. — OVERALL  DIMENSIONS  OF  AIR-BLAST  TRANSFORMERS. 


Rated  Output. 

Periodicity 
in  Cycles 
per  sec. 

Leading  Dimensions  in  mm. 

Weight 
in  tons. 

A. 

B. 

c. 

500  kva 

25 

2200 

1400 

1200 

5 

50 

2150 

1300 

1100 

4 

1000  kva 

25 

2600 

1600 

1400 

7 

50 

2500 

1500 

1300 

6 

1500  kva 

25 

— 

— 

— 

10 

50 

— 

— 

— 

9 

In  Fig.  92  is  shown  a  view  of  a  50-cycle  WestingLouse 
air-blast  transformer  for  550  kva  supplied  to  the  Brighton 
Corporation. 

For  pressures  above  some  20  000  volts  it  is  not  desirable  to 


'//////////////////////////////////, 

FIG.  93. — Diagram  showing  arrangement  of  transformers  and  blowers. 

employ  air-blast  transformers,  as  the  design  of  the  insulation 
for  pressures  above  20  000  volts  may  be  made  much  more 
effective  when  the  transformer  is  arranged  for  oil  immersion. 
Air-blast  transformers  are,  as  shown  in  Fig.  93,  usually 
installed  in  rows,  over  a  longitudinal  duct  through  which 
air  flows  to  the  transformers.  In  Fig.  94  are  shown  nine 
air-blast  transformers  as  installed  at  a  sub-station  of  the 


160     THE    DESIGN   OF    STATIC   TRANSFORMERS 


Buffalo  Railway  Co.     The  nine  transformers  are  divided  into 
three  groups  of  three  each.     Each  group  is  connected  to  con- 


FORCED-COOLED   TRANSFORMERS  161 

stitute  a  three-phase  transforming  set,  and  one,  two  or  all 
three  groups  are  used  according  to  the  amount  of  the  load 
heing  supplied.  The  power  necessary  for  circulating  the 
required  amount  of  air  varies  considerably  in  different  installa- 
tions, according  to  the  length  and  size  of  the  supply  duct  and 
the  general  arrangements  adopted.  The  blower  rarely  requires 
(even  in  small  installations)  to  have  a  capacity  of  more  than 
1  per  cent,  of  the  aggregate  rated  capacity  of  transformers 
installed,  and  it  is  more  usually,  especially  for  groups  of  very 
large  transformers,  well  down  toward  one-tenth  of  1  per  cent. 
It  is  usually  safe  to  estimate  on  a  motor  whose  capacity  is  one- 
half  of  1  per  cent,  of  the  aggregate  capacity  of  the  transformers 
to  be  cooled.  It  is  important  that  the  duct  or  passage  supply- 
ing the  transformers  shall  be  of  large  size,  and  that  plenty  of 
air  shall  reach  even  the  most  distant  transformers  of  the  group. 
The  velocity  at  which  the  air  flows  along  the  duct  should  be  of 
the  order  of  1  meter  per  second,  and  the  air  pressure  at  the 
transformers  will  need  to  be  some  3  to  4  grams  per  sq  cm 
(some  three-quarters  of  an  ounce  per  sq  in)  or  some  5  to  6 
grams  per  sq  cm  as  delivered  from  the  blower.  The  quantity 
of  air  and  the  power  required  for  500-kva  and  1000-kva  sizes 
will  be  roughly  as  shown  in  Table  17. 

TABLE  17, 


Size  of  Transformer. 

Quantity  of  Air  per  Transformer 
in  cu.  meters  per  sec. 

Ditto  in  cu.  ft.  per  min. 

500  kva 
1000  kva 

•  1,0 
M 

1700 
2400 

Owing  to  the  disastrous  consequences  of  a  prolonged  inter- 
ruption of  the  supply  of  air,  it  is  very  desirable  to  duplicate 
the  air-circulating  apparatus,  and  in  general  every  care  must 
be  exercised  in  providing  for  contingencies.  I  recall  a  case 

S.T.  M 


162     THE   DESIGN   OF    STATIC   TRANSFORMERS 

where  a  bank  of  air-blast  transformers  was  located  in  a  base- 
ment right  below  the  switchboard.  In  installing  the  switch- 
board, various  undesirable  materials  fell  through  into  the 
transformers,  which  had  been  carelessly  left  with  their  top 
dampers  open.  Whether  due  to  this  initial  cause  or  not,  con- 
siderable trouble  was  subsequently  experienced  with  burn-outs 
of  these  transformers.  One  of  them  actually  overheated  to  the 
extent  of  igniting  its  insulating  materials,  and  the  combustion 
was  intensified  by  the  air-blast.  Yet  to  shut  down  the  air  blast 
under  such  circumstances  would  also  intensify  the  heating. 
My  own  opinion  is  that  when  the  air-blast  type  is  used,  it  is 
necessary  to  take  the  very  greatest  care.  Thus  even  the  con- 
tingency of  rats  destroying  the  insulation  or  causing  other 
damage  is  by  no  means  remote,  and  has  constituted  a  serious 
danger  in  certain  important  installations.  The  manufacturers 
of  air-blast  transformers  direct  that  all  accessible  parts  of  such 
transformers  shall  be  given  a  systematic  cleaning  at  intervals 
of  once  a  month  or  thereabouts.  This  cleaning  should  include 
getting  at  the  inside  of  the  transformer  and  wiping  away  dirt 
and  dust  from  the  coils  and  from  the  spaces  between  them, 
Even  if  the  transformer  is  protected  from  the  entrance  of  any 
foreign  matter  through  carelessness,  nevertheless  an  undesirable 
amount  of  dirt  and  fine  dust  will  always  gain  access  to  the 
interior  as  it  will  accompan}^  the  circulating  air.  Compressed- 
air  plant,  enabling  a  considerable  pressure  to  be  directed 
against  remote  parts,  will  be  of  much  assistance  in  cleaning 
air-blast  transformers. 

Forced-Water- Cooled  Oil-Transformers. — In  transformers  for 
outputs  of  500  to  5000  kva  or  more,  the  most-widely-employed 
design  is  that  in  which  the  active  material  is  deeply  immersed 
in  oil  and  has,  arranged  above  it,  a  coil  of  cooling  pipes  through 
which  water  is  circulated.  Such  transformers  are  usually 
enclosed  in  a  heavy  boiler-plate  casing.  The  general  external 
appearance  is  well  illustrated  by  Fig.  95  which  relates  to  a 
Westinghouse  10  000-kva  three-phase  66  000- volt  transformer 


FORCED-COOLED   TRANSFORMERS 


163 


of  the    Pennsylvania    Power   and   Water   Co.      The    boiler- 
plate shell  is  riveted  to  a  cast-iron  base  to  which  the  trans- 


FIG.  95. — 10  000-kva  oil-insulated  water-cooled  West  in-house  transformer. 

former  core  is   secured.     Fig.   96  is    an   interior   view   of  a 
transformer  of  the  same  type,  built  by  the  American  General 

M2 


164     THE   DESIGN   OF    STATIC    TKANSFOKMEBS 

Electric  Co.,  and  also  for  10  000  kva  output.     In  this  view  the 
cooling  coils  have  not  yet  been  placed  in  position.     In  Fig.  97 


FIG.  96. — View, of  the  interior  of  the  American  General  Electric  Co.'s  10  000-kva 
100  000- volt  60-cycle  design  for  a  water-cooled  oil-immersed  transformer 
before  the  cooling  coils  have  been  mounted. 


the  cooling  coils  are  also  seen, 
volts. 


This  transformer  is  for  100  000 


FORCED-COOLED   TRANSFORMERS 


165 


In  Figs.  98  and  99  are  shown  views  of  two  large  oil-immersed, 
water-cooled  transformers  by  the  Westinghouse  Co.     The  first 


FIG.  97. — American  General  Electric  Co.'s  10  000-kva  100  000-volt  design  with 
the  cooling  coils  in  place. 


is  (as  may  be  seen  from  the  terminals)  for  very  high  pressure 
and  small  current,  while  the  second  is   for  low  pressure  and 


166     THE   DESIGN   OF   STATIC   TKANSFOKMEKS 


FIG-  98. — Westinghouse  oil-insulated  water-cooled  transformer  for  high-pressure 
and  small  current. 

large  current.  Fig.  99A  shows  the  interior  of  a  50-cycle  1800- 
kva  water-cooled  oil-immersed  transformer  with  the  cover  in 
place.  The  transformer  is  for  a  primary  pressure  of  55  000  volts. 


FOECED-COOLED   TRANSFORMERS  167 

It  is  preferable  that  the  mechanical  support  of  a  transformer 
shall  be  supplied  entirely  by  the  cast-iron  base,  and  that  there 


FIG.  99.— Westing-house  oil-insulated  water-cooled  transformer  for  low  pressure 
and  large  current. 

shall  be  no  dependence  upon  the  boiler-plate  shell.    Alternative 
suitable  constructions  for  supporting  the  active  material  from 


168     THE    DESIGN   OF    STATIC   TKANSFOKMEBS 


FIG.  99A. — 1800-kva  water-cooled  oil-immersed  transformer  built  by  the 
American  General  Electric  Co. 


FOKCED-COOLED   TKANSFOEMEKS  169 

the  cast-iron  base  are  indicated  in  various  of  the  designs 
illustrated  in  this  chapter. 

The  spiral  cooling-coil  for  the  circulating  water  should  be  of 
brass  with  a  view  to  ensuring  a  minimum  of  corrosion.  Brass 
pipes  for  the  purpose  may  be  thinner  than  iron  pipes,  and  also, 
since  the  heat  conductivity  of  brass  is  greater  than  that  of  iron, 
the  heat  is  more  effectively  abstracted  from  the  transformer  by 
way  of  the  oil,  the  brass  pipes,  and,  finally,  the  circulating  water. 

In  the  bulletins  of  a  transformer-manufacturing  firm  of  wide 
experience,  the  amount  of  circulating  water  required  at  full  load 
(entering  at  a  temperature  of  15°)  is  given  as  approximately 

0,8  gallon  per  minute  for    500-kw  transformers 

1,1         L  M  n  »      1000-kw 

1,5      „         ,;        „         ,,    2000-kw 

A  thermometer  is  often  provided,  which  extends  through  the 
case,  and  by  means  of  which  the  attendant  can  intelligently 
control  the  amount  of  water  supplied.  It  would  be  absolutely 
disadvantageous  to  reduce  the  oil  temperature  below  the 
temperature  of  the  room,  as  this  would  cause  the  transformer 
to  "  sweat." 

It  will  be  of  interest  to  indicate  the  method  of  making 
cooling  calculations  for  a  forced-water-cooled  oil-transformer.1 
Let  us  take  as  an  instance  a  1000-kw  50-cycle  transformer. 
The  core  loss  is  7  kw  and  the  I2  R  loss  at  rated  load  is  also 

/1000  X  100 


7  kw.     Consequently  the  full-load  efficiency  is  v  — 

98,5  per  cent.  To  maintain  a  constant  temperature,  energy 
must  be  transferred  from  the  oil  in  the  case  to  the  water  inside 
the  cooling  pipes  at  the  rate  of  14  kw.  Thus  in  each  hour 
the  water  must  carry  away  14  kelvins  of  energy.  1,16  kelvin 
increases  the  temperature  of  1  ton  of  water  by  1°.  If  it  is 

1  These  calculations  are  quite  similar  to  the  calculations  involved  in  connec- 
tion with  surface  condensers  for  steam-engines.  Such  condenser  calculations 
are  explained  in  Chapter  V.  of  the  author's  "  Heavy  Electrical  Engineering," 
(Constable  &  Co.,  London). 


170     THE   DESIGN   OF    STATIC   TRANSFORMERS 

desired  that  the  temperature  rise  of  the  transformer  shall  be 
not  more  than,  for  instance,  30°,  then  if  the  temperature  of 
the  room  is  20°  we  may  take  (20  -f  30  =)  50°  as  the  tempera- 
ture of  the  oil  in  the  immediate  neighbourhood  of  the  cooling 
pipes.  As  in  the  case  of  steam  condensers,  it  will  not  be 
practicable  to  raise  the  temperature  of  the  water  quite  up  to 
the  temperature  of  the  medium  external  to  the  pipes.  Con- 
sequently if  the  water  enters  the  transformer  at,  say,  18°,  it 
will,  with  a  sufficient  length  of  piping,  leave  the  transformer  at, 

say,  45°.  It  will  thus  have  sustained  a  temperature  rise  of 
(45  —  18  =)  27°,  and  each  ton  will  carry  away  (27  X  1,16  =) 
31,3  kelvins  of  energy.  The  amount  of  water  passing  through 

the  cooling  coil  must  consequently  be  [  5^5  —  )  0,447  tori  per 

\ol,o      / 

hour.     (Since  there  are  220  gallons  in  one  ton  of  water,  this  is 
equal  to  0,447  X  220  =  99  gallons  per  hour,  or  1,65  gallons 
per  minute.) 

If  in  another  instance,  a  temperature  rise  of  40°  is  per- 
mitted, if  the  room  temperature  is  20°,  if  the  water  enters 
at  15°,  and  if  its  final  temperature  attains  to  within  7°  of  the 
temperature  of  the  oil,  then  the  quantity  of  water  would  be 
calculated  as  follows  : — 
Temperature  of  room      .         .         .         ..        .         .         .     20° 

Temperature  rise  of  oil  .         .          .         .         . ,        ,         .     40° 

Ultimate  temperature  of  oil     .         .         .         (20  +  40  =)  60° 
Entrance  temperature  of  water         .....     15° 

Exit  temperature  of  water       .         .         .  (60  -  7  =)  53° 

Temperature  rise  of  water  .  .  .  (53  —  15  =)  38° 
Energy  absorbed  by  each  ton  of  water  (1>16  X  38  =)  44 

kelvins 


Weight  of  water  per  hour  ...  (44^5  — )  0>319  ton 
Volume  of  water  per  hour  .  (0,319  X  220  =)  70  gallons 
Volume  of  water  per  minute  .  .  (^  =  j  1,17  gallons 


FOKCED-COOLED   TKANSFOKMERS  171 

It  is  thus  evident  that  each  case  must  be  separately  considered. 
One  gallon  is  equal  to  4530  cu  cm,  and  the  volume  of  water  per 
second  may  in  the  last  case  be  expressed  as 

1,17  X  4530 

or.        -  =  88  cu  cm. 
bO 

If  we  adopt  0,5  meter  per  second  for  the  speed  of  flow  of  the 

00 

water,  then  the  area  of  the  pipe  must  be  ^-  =  1,76  sq  cm  and 

ou 

the  internal  diameter  must  be  15  mm.  The  thickness  of  the 
brass  .tubing  will  usually  be  about  1,25  mm.  Consequently 
the  external  diameter  is  17,5  mm  and  the  external  surface  per 
meter  length  of  tubing  is  (10  X  0,175  X  IT  =)  5,5  sq  dm. 
The  rate  of  transference  of  heat  from  one  medium  to  another 
is  a  matter  which  has  not  yet  been  reduced  to  a  reliable  basis 
and  is  still  usually  determined  by  experiments.  It  depends 
upon  the  speed  of  flow  of  the  water  and  on  other  variables. 
Let  us  take  it  at  1,5  watt  per  degree  per  sq  dm  of  heating 
surface.  In  our  case  we  are  dealing  with  14  000  watts.  The 
mean  difference  of  temperature  between  the  oil  and  the  water 
is 

60  _  58  +  15  =  26°. 

a 

Consequently  the  water  will  take  up  the  heat  at  the  rate  of 
(26  X  1,5  —  )  39  watts  per  sq  dm,  and  we  shall  require  to 


provide  (  —  ^  —  =  j  360  sq  dm  or  a  total  length  of  [jr*-  =J 

66  meters  of  tubing. 

In  a  paper  read  before  the  Schenectady  section  of  the 
American  Institute  of  Electrical  Engineers,  Tobey  describes 
the  arrangement  illustrated  in  Fig.  100,  in  which  a  transformer 
is  provided  with  a  cylindrical  barrier  interposed  between  the 
transformer  and  the  external  cylindrical  sides  of  the  case. 
This  barrier  does  not  extend  quite  down  to  the  bottom  of  the 
case.  The  oil  adjacent  to  the  core  and  windings  becomes 


172     THE   DESIGN   OF    STATIC   TRANSFORMERS 

heated  and  rises  to  the  upper  part  of  the  transformer.  By 
means  of  a  small  motor  the  oil  is  pumped  over  to  the  part 
exterior  to  the  barrier  where  it  cools  and  fall  to  the  bottom, 
ready  to  start  on  another  journey  through  the  transformer  and 
to  abstract  further  heat  from  the  active  material. 

Forced-Oil-Cooled     Transformers. — As     an     alternative     to 
employing  a  coil  of  tubes  in  the  oil  and  circulating  cooling 


FIG.  100. — Oil-immersed  transformer  provided  with  cylindrical  barrier  to 
promote  circulation. 

water  through  the  coil,  there  are  occasions  where  it  is  more 
advantageous  to  pump  the  oil  out  of  the  transformer,  cool  it, 
and  pump  it  back  again.  In  the  arrangement  shown  in  Fig. 
101  the  hot  oil  leaving  the  transformer  at  B,  is,  by  means  of 
the  pump  A,  forced  through  the  spiral  pipe  C,  and  is  then 
forced  into  the  transformer  again  at  D.  In  its  passage 
through  C  the  heat  is  transferred  from  the  oil  to  the  cooling 
water  which  is  forced  into  and  from  the  tank  E  by  the  pump  F 
driven  by  the  motor  G.  The  difference  in  temperature  between 


FOKCED-COOLED   TRANSFORMERS 


173 


the  oil  when  entering  and  when  leaving  the  transformer  is 
usually  only  allowed  to  be  some  10°.  The  specific  gravity  of 
transformer  oil  is  about  0,9  and  its  specific  heat  is  about  0,7s.1 
Consequently  (1,16  X  0,75  X  0,9  =)  0,78  kelvin  is  absorbed 
by  1  cu  m  of  oil  when  its  temperature  is  raised  1°.  In  our 
transformer  the  temperature  of  the  oil  is  raised  10°,  absorbing 
7,8  kelvins  per  cu  m.  Thus  the  quantity  requiring  to  be 


circulated  is 


,o 


1,80  cu  m,  or   (1,80   X  220  =)   400 


gallons  per  hour,  or  6,7  gallons  per  minute. 


FIG-.  101. — Forced-oil-cooled  transformer  and  accessory  plant. 

In  forced-oil-cooled  transformers  there  arises  the  important 
question  whether  each  transformer  shall  be  provided  with  its 
own  complete  oil-circulating  and  cooling  plant,  or  whether  all 
the  transformers  in  the  installation  shall  be  supplied  from  a 
common  oil  main.  Although  the  latter  plan  leads  to  the 
lowest  first  cost,  the  former  is  to  be  preferred,  since,  in  the 
event  of  a  breakdown  anywhere,  it  is  important  that  the  entire 
plant  shall  not  be  incapacitated.  Oil  is  greatly  affected  by  the 
admixture  of  impurity  or  moisture,  and  if  any  single  trans- 
former of  a  bank  of  transformers  goes  wrong,  with  the  con- 
sequence of  impairing  the  quality  of  any  oil  entering  it,  then  it 

1  See  Table  VI.  on  p.  11  and  Example  VII.  on  p.  13  of  the  author's  "  Heavy 
Electrical  Engineering  "  (Constable  &  Co.,  London). 


174    THE   DESIGN   OF   STATIC   TRANSFORMERS 

is  important  that  the  damaged  oil  shall  not  gain  access  to  any 
of  the  other  transformers. 

While  for  a  time,  considerable  attention  was  given  to  forced- 
oil-cooled  transformers,  and  the  plan  was  adopted  on  several 
installations,  it  has  often  been  found  that  the  extra  cost  of 
the  auxiliary  plant  required,  largely  offsets  any  advantages, 
and  the  present  tendency  in  large  transformers  is  toward  the 
employment  of  oil-immersed  transformers  with  water  cooling 
by  means  of  coils  of  piping  within  the  transformer  through 
which  the  water  circulates.  Nevertheless  the  oil-circulating 
proposition  affords  a  sound  and  appropriate  solution  in  many 
instances. 


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